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Maths-

General

Easy

Question

If $left parenthesis n plus 1 right parenthesis P subscript 5 colon to the power of n P subscript 5 equals 3 colon 2$ then n is:

8
14
10
6

hint Hint:

To find the value of n in $left parenthesis n plus 1 right parenthesis P subscript 5 colon to the power of n P subscript 5 equals 3 colon 2$ we will first use the formula $P with r below and n on top equals fraction numerator n factorial over denominator left parenthesis n minus r right parenthesis factorial end fraction$ then after putting the values in the formula we will get the value of n.

The correct answer is: 14

Given, $left parenthesis n plus 1 right parenthesis P subscript 5 colon to the power of n P subscript 5 equals 3 colon 2$
$rightwards double arrow fraction numerator begin display style fraction numerator left parenthesis n plus 1 right parenthesis factorial over denominator left parenthesis n plus 1 minus 5 right parenthesis factorial end fraction end style over denominator begin display style fraction numerator n factorial over denominator left parenthesis n minus 5 right parenthesis factorial end fraction end style end fraction equals 3 over 2 rightwards double arrow fraction numerator left parenthesis n plus 1 right parenthesis factorial over denominator left parenthesis n minus 4 right parenthesis factorial end fraction cross times fraction numerator left parenthesis n minus 5 right parenthesis factorial over denominator n factorial end fraction equals 3 over 2 rightwards double arrow fraction numerator left parenthesis n plus 1 right parenthesis n factorial over denominator left parenthesis n minus 4 right parenthesis left parenthesis n minus 5 right parenthesis factorial end fraction cross times fraction numerator left parenthesis n minus 5 right parenthesis factorial over denominator n factorial end fraction equals 3 over 2 rightwards double arrow fraction numerator n plus 1 over denominator n minus 4 end fraction equals 3 over 2 rightwards double arrow 2 left parenthesis n plus 1 right parenthesis equals 3 left parenthesis n minus 4 right parenthesis rightwards double arrow 2 n plus 2 equals 3 n minus 12 rightwards double arrow n equals 14$

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