image

    Have a query? Ask a Tutor!!

    Access to best educators and exclusive paper discussions

    Offsite CampusTurito Championship

    Can’t find what you’re looking for?

    Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

    • Homework- One to One Solutions
    • Understand concepts to solve better
    • Get your doubts solved instantly
    Maths-
    General
    Easy

    Question

    The number of different signals that can be made by 5 flags from 8 flags of different colours is :

    1. 6720    
    2. blank to the power of 8 end exponent C subscript 5 end subscript    
    3. 8 to the power of 5 end exponent    
    4. 5 to the power of 8 end exponent    

    hintHint:

    W e space a r e space p r o v i d e d space w i t h space 8 space space f l a g s space o f space d i f f e r e n t space c o l o u r s space a n d space 5 space space f l a g s. W e space n e e d space t o space f i n d space t h e space t o t a l space n u m b e r space o f space s i g n a l s space t h a t space c a n space b e space m a d e space b y space t h e space n u m b e r space o f space a r r a n g e m e n t s space o f space 8 space space f l a g s space b y space t a k i n g space 5 space space f l a g s space a t space a space t i m e. A r r a n g i n g space t h i n g s space i s space c a l l e d space p e r m u t a t i o n comma space t h u s space w e space c a n space c l e a r l y space s a y space t h a t space t h e space g i v e n space q u e s t i o n space i s space b a s e d space o n space t h e space t o p i c space “ p e r m u t a t i o n ”. space H e r e space w e space h a v e space t o space a r r a n g e space 8 space space f l a g s space t a k e n space 5 space space f l a g s space a t space a space t i m e space w h i c h space i s space e q u i v a l e n t space t o space f i l l i n g space 8 space space f l a g s space p l a c e d space o u t space o f space 5 space space f l a g s. space space F o r space t h a t space w e space h a v e space t h e space f o r m u l a space o f space p e r m u t a t i o n colon space scriptbase P subscript r end scriptbase presuperscript n space.

    The correct answer is: 6720

      D e t a i l e d space S o l u t i o n W e space h a v e space b e e n space t o l d space t h a t space t h e r e space a r e space 8 space space f l a g s space o f space d i f f e r e n t space c o l o u r s space b y space t a k i n g space 5 space space f l a g s space a t space a space t i m e. T h u s space t h e space t o t a l space n u m b e r space o f space f l a g s space n equals 8 space space a n d space f l a g s space t o space b e space t a k e n space a t space a space t i m e space r equals 5 space. space B y space a p p l y i n g space t h e space p e r m u t a t i o n space f o r m u l a space equals scriptbase P subscript r end scriptbase presuperscript n space equals scriptbase P subscript 5 end scriptbase presuperscript 8

      B y space a p p l y i n g space i n space p e r m u t a t i o n comma equals fraction numerator space 8 factorial over denominator left parenthesis 8 minus 5 right parenthesis factorial space space end fraction S u b t r a c t i n g space t h e space v a l u e s space i n space d e n o m i n a t o r comma equals space space fraction numerator 8 factorial over denominator 3 factorial space space end fraction E x p a n d i n g space t h e space f a c t o r i a l comma equals space fraction numerator 8 cross times 7 cross times 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator 3 cross times 2 cross times 1 space space end fraction space equals space 6720 T h u s comma space space t h e space r e q u i r e d space n u m b e r space o f space s i g n a l s space c a n space b e space m a d e space b y space 5 space space f l a g s space f r o m space 8 space space f l a g s space o f space d i f f e r e n t space c o l o u r s space i s space 6720 space.

      Each of the different arrangements which can be made by taking some or all of a number of things at a time is called permutation. 
      space T h e space n u m b e r space o f space p e r m u t a t i o n space w i t h o u t space a n y space r e p e t i t i o n space s t a t e s space t h a t space a r r a n g i n g space n space space o b j e c t s space t a k e n space r space space a t space a space t i m e space i s space e q u i v a l e n t space t o space f i l l i n g space r space space p l a c e s space o u t space o f space n space space t h i n g s space equals space n left parenthesis n minus 1 right parenthesis left parenthesis n minus 2 right parenthesis... left parenthesis n minus top enclose r minus 1 end enclose right parenthesis space space space w a y s equals fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction space equals space scriptbase P subscript r end scriptbase presuperscript n


      W e space c a n space a l s o space s a y space t h a t comma space space scriptbase P subscript r end scriptbase presuperscript n equals space n left parenthesis n minus 1 right parenthesis left parenthesis n minus 2 right parenthesis... left parenthesis n minus r plus 1 right parenthesis space space comma space t h u s comma scriptbase P subscript 5 end scriptbase presuperscript 8 equals space 8 cross times 7 cross times 6 cross times 5 cross times 4 space equals space 6720 space.

      Thus we can say that the permutation concerns both the selection and the arrangement of the selected things in all possible ways.

      Related Questions to study

      General
      Maths-

      If fraction numerator x to the power of 2 end exponent plus x plus 1 over denominator x to the power of 2 end exponent plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent end fraction then A-B=

      If fraction numerator x to the power of 2 end exponent plus x plus 1 over denominator x to the power of 2 end exponent plus 2 x plus 1 end fraction equals A plus fraction numerator B over denominator x plus 1 end fraction plus fraction numerator C over denominator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent end fraction then A-B=

      Maths-General
      General
      Maths-

      fraction numerator x plus 1 over denominator left parenthesis 2 x minus 1 right parenthesis left parenthesis 3 x plus 1 right parenthesis end fraction equals fraction numerator A over denominator 2 x minus 1 end fraction plus fraction numerator B over denominator 3 x plus 1 end fraction, then 16 A plus 9 B equals

      fraction numerator x plus 1 over denominator left parenthesis 2 x minus 1 right parenthesis left parenthesis 3 x plus 1 right parenthesis end fraction equals fraction numerator A over denominator 2 x minus 1 end fraction plus fraction numerator B over denominator 3 x plus 1 end fraction, then 16 A plus 9 B equals

      Maths-General
      General
      Maths-

      If fraction numerator x to the power of 2 end exponent minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent minus 5 x plus 6 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x minus 2 end fraction plus fraction numerator K over denominator x minus 3 end fraction then K=

      If fraction numerator x to the power of 2 end exponent minus 10 x plus 13 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent minus 5 x plus 6 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator x minus 2 end fraction plus fraction numerator K over denominator x minus 3 end fraction then K=

      Maths-General
      parallel
      General
      Maths-

      If the remainders of the polynomial f left parenthesis x right parenthesis when divided by x plus 1 and x minus 1 are 7,3 then the remainder of f left parenthesis x right parenthesis when devided by x to the power of 2 end exponent minus 1 is

      If the remainders of the polynomial f left parenthesis x right parenthesis when divided by x plus 1 and x minus 1 are 7,3 then the remainder of f left parenthesis x right parenthesis when devided by x to the power of 2 end exponent minus 1 is

      Maths-General
      General
      Maths-

      If fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis left parenthesis c x plus d right parenthesis end fraction equals fraction numerator A over denominator a x plus b end fraction plus fraction numerator B over denominator c x plus d end fraction then fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis to the power of 2 end exponent left parenthesis c x plus d right parenthesis end fraction equals

      If fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis left parenthesis c x plus d right parenthesis end fraction equals fraction numerator A over denominator a x plus b end fraction plus fraction numerator B over denominator c x plus d end fraction then fraction numerator 1 over denominator left parenthesis a x plus b right parenthesis to the power of 2 end exponent left parenthesis c x plus d right parenthesis end fraction equals

      Maths-General
      General
      Maths-

      The partial fractions of fraction numerator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent over denominator x open parentheses x to the power of 2 end exponent plus 1 close parentheses end fraction are

      The partial fractions of fraction numerator left parenthesis x plus 1 right parenthesis to the power of 2 end exponent over denominator x open parentheses x to the power of 2 end exponent plus 1 close parentheses end fraction are

      Maths-General
      parallel
      General
      Maths-

      The partial fractions of fraction numerator 1 over denominator x to the power of 3 end exponent left parenthesis x plus 2 right parenthesis end fraction are

      The partial fractions of fraction numerator 1 over denominator x to the power of 3 end exponent left parenthesis x plus 2 right parenthesis end fraction are

      Maths-General
      General
      Maths-

      fraction numerator 3 x to the power of 2 end exponent plus x plus 1 over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end fraction plus fraction numerator C over denominator left parenthesis x minus 1 right parenthesis to the power of 3 end exponent end fraction plus fraction numerator D over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction then A plus B minus C plus D equals

      fraction numerator 3 x to the power of 2 end exponent plus x plus 1 over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B over denominator left parenthesis x minus 1 right parenthesis to the power of 2 end exponent end fraction plus fraction numerator C over denominator left parenthesis x minus 1 right parenthesis to the power of 3 end exponent end fraction plus fraction numerator D over denominator left parenthesis x minus 1 right parenthesis to the power of 4 end exponent end fraction then A plus B minus C plus D equals

      Maths-General
      General
      Maths-

      The partial fractions of fraction numerator x to the power of 2 end exponent over denominator open parentheses x to the power of 2 end exponent plus a to the power of 2 end exponent close parentheses open parentheses x to the power of 2 end exponent plus b to the power of 2 end exponent close parentheses end fraction are

      The partial fractions of fraction numerator x to the power of 2 end exponent over denominator open parentheses x to the power of 2 end exponent plus a to the power of 2 end exponent close parentheses open parentheses x to the power of 2 end exponent plus b to the power of 2 end exponent close parentheses end fraction are

      Maths-General
      parallel
      General
      Maths-

      The partial fractions of fraction numerator 6 x to the power of 4 end exponent plus 5 x to the power of 3 end exponent plus x to the power of 2 end exponent plus 5 x plus 2 over denominator 1 plus 5 x plus 6 x to the power of 2 end exponent end fraction are

      The partial fractions of fraction numerator 6 x to the power of 4 end exponent plus 5 x to the power of 3 end exponent plus x to the power of 2 end exponent plus 5 x plus 2 over denominator 1 plus 5 x plus 6 x to the power of 2 end exponent end fraction are

      Maths-General
      General
      Maths-

      If fraction numerator x to the power of 4 end exponent over denominator left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis left parenthesis x minus c right parenthesis end fraction equals P left parenthesis x right parenthesis plus fraction numerator A over denominator x minus a end fraction plus fraction numerator B over denominator x minus b end fraction plus fraction numerator C over denominator x minus c end fraction then P left parenthesis x right parenthesis equals

      If fraction numerator x to the power of 4 end exponent over denominator left parenthesis x minus a right parenthesis left parenthesis x minus b right parenthesis left parenthesis x minus c right parenthesis end fraction equals P left parenthesis x right parenthesis plus fraction numerator A over denominator x minus a end fraction plus fraction numerator B over denominator x minus b end fraction plus fraction numerator C over denominator x minus c end fraction then P left parenthesis x right parenthesis equals

      Maths-General
      General
      Maths-

      Let a,b,c such that fraction numerator 1 over denominator left parenthesis 1 minus x right parenthesis left parenthesis 1 minus 2 x right parenthesis left parenthesis 1 minus 3 x right parenthesis end fraction equals fraction numerator a over denominator 1 minus x end fraction plus fraction numerator b over denominator 1 minus 2 x end fraction plus fraction numerator c over denominator 1 minus 3 x end fraction then ,fraction numerator a over denominator 1 end fraction plus fraction numerator b over denominator 3 end fraction plus fraction numerator c over denominator 5 end fraction equals?

      Let a,b,c such that fraction numerator 1 over denominator left parenthesis 1 minus x right parenthesis left parenthesis 1 minus 2 x right parenthesis left parenthesis 1 minus 3 x right parenthesis end fraction equals fraction numerator a over denominator 1 minus x end fraction plus fraction numerator b over denominator 1 minus 2 x end fraction plus fraction numerator c over denominator 1 minus 3 x end fraction then ,fraction numerator a over denominator 1 end fraction plus fraction numerator b over denominator 3 end fraction plus fraction numerator c over denominator 5 end fraction equals?

      Maths-General
      parallel
      General
      Maths-

      If fraction numerator 2 x plus 1 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent plus 2 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B x plus c over denominator x to the power of 2 end exponent plus 2 end fraction then B=

      If fraction numerator 2 x plus 1 over denominator left parenthesis x minus 1 right parenthesis open parentheses x to the power of 2 end exponent plus 2 close parentheses end fraction equals fraction numerator A over denominator x minus 1 end fraction plus fraction numerator B x plus c over denominator x to the power of 2 end exponent plus 2 end fraction then B=

      Maths-General
      General
      Maths-

      If the remainders of the polynomial f(x) when divided by x minus 1 comma x minus 2 are 2,5 then the remainder of f left parenthesis x right parenthesis when divided by left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis is

      If the remainders of the polynomial f(x) when divided by x minus 1 comma x minus 2 are 2,5 then the remainder of f left parenthesis x right parenthesis when divided by left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis is

      Maths-General
      General
      Maths-

      Assertion : f left parenthesis x right parenthesis equals s g n invisible function application left parenthesis x minus vertical line x vertical line right parenthesis can never become positive.
      Reason : f(x) = sgn x is always a positive function.

      Assertion : f left parenthesis x right parenthesis equals s g n invisible function application left parenthesis x minus vertical line x vertical line right parenthesis can never become positive.
      Reason : f(x) = sgn x is always a positive function.

      Maths-General
      parallel

      card img

      With Turito Academy.

      card img

      With Turito Foundation.

      card img

      Get an Expert Advice From Turito.

      Turito Academy

      card img

      With Turito Academy.

      Test Prep

      card img

      With Turito Foundation.