Maths-

General

Easy

Question

A tea party is arranged of 16 persons along two sides of a long table with 8 chairs on each side. 4 men wish to sit on one particular side and 2 on the other side. In how many ways can they be seated ?

⁸P₄ × ⁸P₂
210 $\times$ 8! $\times$ 8!
⁸P₄ × 10!
None of these

hint Hint:

In this question we have in total 16 seats with 8 on each side of the table. Firstly make these 4+2=6 people sit who have special demand in sitting arrangements. Now when these 6 people are taken care of we are left with 10 people and 4 seats on one side and 6 seats on the other side, use this concept to get the answer.

The correct answer is: 210 $cross times$ 8! $cross times$ 8!

Detailed Solution
There are 16 people for the tea party.

People sit along a long table with 8 chairs on each side.

Out of 16, 4 people sit on a particular side and 2 sit on the other side.

Therefore first we will make sitting arrangements for those 6 persons who want to sit on some specific side.
Now we have remaining (16 - 6) =10 persons to arrange and out of 10, six people can sit on one side as only 6 seats will be reaming after making 2 people sit on one side on special demand and 4 people on other side as 4 people are already being seated on one side on special demand. (Take into consideration that one side has only 8 seats)
The number of ways of choosing 6 people out of 10 are $scriptbase C subscript 6 end scriptbase presuperscript 10$ now there are 4 people remaining and they will automatically place in those 4 seats available on the other side therefore total arrangement for those four people are $scriptbase C subscript 4 space equals 1 end scriptbase presuperscript 4$
And now all the 16 people are placed in their seats according to the constraints.

Now we have to arrange them.

So, the number of ways of arranging 8 people out of 16 on one side and the rest 8 people on other side is (8! $cross times$ 8!)
$S o comma space a space p o s s i b l e space n u m b e r space o f space a r r a n g e m e n t s space w i l l space b e space space rightwards double arrow space scriptbase C subscript 6 space cross times space scriptbase C subscript 4 space cross times end scriptbase presuperscript 4 space 8 factorial space cross times space 8 factorial end scriptbase presuperscript 10$
$N o w space a s space w e space k n o w space scriptbase C subscript r space end subscript end scriptbase presuperscript n equals space fraction numerator n factorial over denominator r factorial left parenthesis n minus r right parenthesis factorial. end fraction$

$S o comma space space scriptbase C subscript 6 end scriptbase presuperscript 10 space equals space fraction numerator 10 factorial over denominator 6 factorial space 4 factorial end fraction space equals space 210 a n d space space scriptbase C subscript 4 space equals space 1 end scriptbase presuperscript 4$

So, total number of arrangements is $space equals space space 210 space cross times space 8 factorial space cross times 8 factorial$

Whenever we face such types of problems the key point is to make special arrangements for the people who are in need of it, then arrange the remaining. Now combination comes with permutation as there are possibilities of these 8 people sitting on one side to rearrange. Thus this concept into consideration, to get through the answer.

If ^(m+n)P₂ = 56 and ^m–nP₂ = 12 then (m, n) equals-

Maths-General

General

physics-

A thin uniform annular disc (see figure) of mass $M$ has outer radius $4 R$ and inner radius $3 R$ . The work required to take a unit mass from point $P$ on its axis to infinity is

physics-General

General

physics-

The two bodies of mass $m subscript 1 end subscript$ and $m subscript 2 end subscript left parenthesis m subscript 1 end subscript greater than m subscript 2 end subscript right parenthesis$ respectively are tied to the ends of a massless string, which passes over a light and frictionless pulley. The masses are initially at rest and the released. Then acceleration of the centre of mass of the system is

physics-General

General

maths-

If $x equals 1 plus 3 a plus 6 a squared plus 10 a cubed plus midline horizontal ellipsis.$ to $straight infinity$ terms, $vertical line a vertical line less than 1 comma y equals 1 plus 4 a plus 10 a squared plus 20 a cubed plus midline horizontal ellipsis$ $straight infinity$ terms, $vertical line a vertical line less than 1$ , then $x colon y$

maths-General

General

Maths-

The coefficient of $x to the power of negative n end exponent$ in $left parenthesis 1 plus x right parenthesis to the power of n end exponent open parentheses 1 plus fraction numerator 1 over denominator x end fraction close parentheses to the power of n end exponent$ is

Maths-General

General

maths-

$open parentheses 1 plus x plus x squared plus horizontal ellipsis plus x to the power of p close parentheses to the power of n equals a subscript 0 plus a subscript 1 x plus a subscript 2 x squared plus horizontal ellipsis$ $plus a subscript n p end subscript x to the power of n p end exponent not stretchy rightwards double arrow a subscript 1 plus 2 a subscript 2 plus 3 a subscript 3 plus horizontal ellipsis plus n p$

maths-General

General

chemistry-

Compounds (A) and (B) are –

chemistry-General

General

Maths-

$2 times C subscript 0 plus 5 times C subscript 1 plus 8 times C subscript 2 plus horizontal ellipsis plus left parenthesis 2 plus 3 n right parenthesis times C subscript n equals$

Maths-General

General

maths-

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:

maths-General

General

Maths-

If one root of the equation $a x squared plus b x plus c equals 0$ is reciprocal of the one of the roots of equation $a subscript 1 x squared plus b subscript 1 x plus c subscript 1 equals 0$ then

Maths-General

General

Maths-

If the quadratic equation $a x squared plus 2 c x plus b equals 0$ and $a x squared plus 2 b x plus c equals 0 left parenthesis b not equal to c right parenthesis$ have a common root then $a plus 4 b plus 4 c$ is equal to

Maths-General

General

physics-

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on frictionless horizontal surface. An impulsive force gives a velocity of 14 $m s to the power of negative 1 end exponent$ to the heavier block in the direction of the lighter block. The velocity of centre of mass of the system at that very moment is

physics-General

General

Maths-

In a Δabc if b+c=3a then $cot invisible function application straight B over 2 times cot invisible function application straight C over 2$ has the value equal to –

Maths-General

General

Maths-

In a $capital delta A B C open parentheses fraction numerator a to the power of 2 end exponent over denominator sin invisible function application A end fraction plus fraction numerator b to the power of 2 end exponent over denominator sin invisible function application B end fraction plus fraction numerator c to the power of 2 end exponent over denominator sin invisible function application C end fraction close parentheses times s i n invisible function application fraction numerator A over denominator 2 end fraction s i n invisible function application fraction numerator B over denominator 2 end fraction s i n invisible function application fraction numerator C over denominator 2 end fraction$ simplifies to

Maths-General

General

Maths-

In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :

Maths-General

Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

A tea party is arranged of 16 persons along two sides of a long table with 8 chairs on each side. 4 men wish to sit on one particular side and 2 on the other side. In how many ways can they be seated ?

⁸P₄ × ⁸P₂
210 $\times$ 8! $\times$ 8!
⁸P₄ × 10!
None of these

The correct answer is: 210 $cross times$ 8! $cross times$ 8!

Related Questions to study

If ^(m+n)P₂ = 56 and ^m–nP₂ = 12 then (m, n) equals-

If ^(m+n)P₂ = 56 and ^m–nP₂ = 12 then (m, n) equals-

A thin uniform annular disc (see figure) of mass $M$ has outer radius $4 R$ and inner radius $3 R$ . The work required to take a unit mass from point $P$ on its axis to infinity is

A thin uniform annular disc (see figure) of mass $M$ has outer radius $4 R$ and inner radius $3 R$ . The work required to take a unit mass from point $P$ on its axis to infinity is

The coefficient of $x to the power of negative n end exponent$ in $left parenthesis 1 plus x right parenthesis to the power of n end exponent open parentheses 1 plus fraction numerator 1 over denominator x end fraction close parentheses to the power of n end exponent$ is

The coefficient of $x to the power of negative n end exponent$ in $left parenthesis 1 plus x right parenthesis to the power of n end exponent open parentheses 1 plus fraction numerator 1 over denominator x end fraction close parentheses to the power of n end exponent$ is

Compounds (A) and (B) are –

Compounds (A) and (B) are –

$2 times C subscript 0 plus 5 times C subscript 1 plus 8 times C subscript 2 plus horizontal ellipsis plus left parenthesis 2 plus 3 n right parenthesis times C subscript n equals$

$2 times C subscript 0 plus 5 times C subscript 1 plus 8 times C subscript 2 plus horizontal ellipsis plus left parenthesis 2 plus 3 n right parenthesis times C subscript n equals$

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:

If one root of the equation $a x squared plus b x plus c equals 0$ is reciprocal of the one of the roots of equation $a subscript 1 x squared plus b subscript 1 x plus c subscript 1 equals 0$ then

If one root of the equation $a x squared plus b x plus c equals 0$ is reciprocal of the one of the roots of equation $a subscript 1 x squared plus b subscript 1 x plus c subscript 1 equals 0$ then

If the quadratic equation $a x squared plus 2 c x plus b equals 0$ and $a x squared plus 2 b x plus c equals 0 left parenthesis b not equal to c right parenthesis$ have a common root then $a plus 4 b plus 4 c$ is equal to

If the quadratic equation $a x squared plus 2 c x plus b equals 0$ and $a x squared plus 2 b x plus c equals 0 left parenthesis b not equal to c right parenthesis$ have a common root then $a plus 4 b plus 4 c$ is equal to

In a Δabc if b+c=3a then $cot invisible function application straight B over 2 times cot invisible function application straight C over 2$ has the value equal to –

In a Δabc if b+c=3a then $cot invisible function application straight B over 2 times cot invisible function application straight C over 2$ has the value equal to –

In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :

In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :

With Turito Academy.

With Turito Foundation.

Get an Expert Advice From Turito.

Turito Academy

With Turito Academy.

Test Prep

With Turito Foundation.

Courses

Quick Links

Follow Us at

Support

Download App

Courses

Quick Links

Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

A tea party is arranged of 16 persons along two sides of a long table with 8 chairs on each side. 4 men wish to sit on one particular side and 2 on the other side. In how many ways can they be seated ?

8P4 × 8P2 210 8! 8! 8P4 × 10! None of these

The correct answer is: 210 8! 8!

Related Questions to study

If (m+n) P2 = 56 and m–nP2 = 12 then (m, n) equals-

If (m+n) P2 = 56 and m–nP2 = 12 then (m, n) equals-

A thin uniform annular disc (see figure) of mass has outer radius and inner radius . The work required to take a unit mass from point on its axis to infinity is

A thin uniform annular disc (see figure) of mass has outer radius and inner radius . The work required to take a unit mass from point on its axis to infinity is

The two bodies of mass and respectively are tied to the ends of a massless string, which passes over a light and frictionless pulley. The masses are initially at rest and the released. Then acceleration of the centre of mass of the system is

The two bodies of mass and respectively are tied to the ends of a massless string, which passes over a light and frictionless pulley. The masses are initially at rest and the released. Then acceleration of the centre of mass of the system is

If to terms, terms, , then

If to terms, terms, , then

The coefficient of in is

The coefficient of in is

Compounds (A) and (B) are –

Compounds (A) and (B) are –

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:

A triangle is inscribed in a circle. The vertices of the triangle divide the circle into three arcs of length 3, 4 and 5 units. Then area of the triangle is equal to:

If one root of the equation is reciprocal of the one of the roots of equation then

If one root of the equation is reciprocal of the one of the roots of equation then

If the quadratic equation and have a common root then is equal to

If the quadratic equation and have a common root then is equal to

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on frictionless horizontal surface. An impulsive force gives a velocity of 14 to the heavier block in the direction of the lighter block. The velocity of centre of mass of the system at that very moment is

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on frictionless horizontal surface. An impulsive force gives a velocity of 14 to the heavier block in the direction of the lighter block. The velocity of centre of mass of the system at that very moment is

In a Δabc if b+c=3a then has the value equal to –

In a Δabc if b+c=3a then has the value equal to –

In a simplifies to

In a simplifies to

In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :

In a triangle ABC, a: b: c = 4: 5: 6. Then 3A + B equals to :

With Turito Academy.

With Turito Foundation.

Get an Expert Advice From Turito.

Turito Academy

With Turito Academy.

Test Prep

With Turito Foundation.

Courses

Quick Links

⁸P₄ × ⁸P₂
210 $\times$ 8! $\times$ 8!
⁸P₄ × 10!
None of these

The correct answer is: 210 $cross times$ 8! $cross times$ 8!

If ^(m+n)P₂ = 56 and ^m–nP₂ = 12 then (m, n) equals-

If ^(m+n)P₂ = 56 and ^m–nP₂ = 12 then (m, n) equals-

A thin uniform annular disc (see figure) of mass $M$ has outer radius $4 R$ and inner radius $3 R$ . The work required to take a unit mass from point $P$ on its axis to infinity is

A thin uniform annular disc (see figure) of mass $M$ has outer radius $4 R$ and inner radius $3 R$ . The work required to take a unit mass from point $P$ on its axis to infinity is

The coefficient of $x to the power of negative n end exponent$ in $left parenthesis 1 plus x right parenthesis to the power of n end exponent open parentheses 1 plus fraction numerator 1 over denominator x end fraction close parentheses to the power of n end exponent$ is

The coefficient of $x to the power of negative n end exponent$ in $left parenthesis 1 plus x right parenthesis to the power of n end exponent open parentheses 1 plus fraction numerator 1 over denominator x end fraction close parentheses to the power of n end exponent$ is

If one root of the equation $a x squared plus b x plus c equals 0$ is reciprocal of the one of the roots of equation $a subscript 1 x squared plus b subscript 1 x plus c subscript 1 equals 0$ then

If one root of the equation $a x squared plus b x plus c equals 0$ is reciprocal of the one of the roots of equation $a subscript 1 x squared plus b subscript 1 x plus c subscript 1 equals 0$ then

If the quadratic equation $a x squared plus 2 c x plus b equals 0$ and $a x squared plus 2 b x plus c equals 0 left parenthesis b not equal to c right parenthesis$ have a common root then $a plus 4 b plus 4 c$ is equal to

If the quadratic equation $a x squared plus 2 c x plus b equals 0$ and $a x squared plus 2 b x plus c equals 0 left parenthesis b not equal to c right parenthesis$ have a common root then $a plus 4 b plus 4 c$ is equal to

In a Δabc if b+c=3a then $cot invisible function application straight B over 2 times cot invisible function application straight C over 2$ has the value equal to –

In a Δabc if b+c=3a then $cot invisible function application straight B over 2 times cot invisible function application straight C over 2$ has the value equal to –