Question

find n if 2nP3=100×nP2

Answer 1

Answer: The value of n is 13.

Step-by-step explanation: We are all familiar with the concepts of permutaion and combination. To solve the given equality for n, we have to apply the formula for permutation of a number 'n' taking 'r' at a time.

We are given to find the value of n if

$\dfrac{(2n)!}{(2n-3)!}=100\times \dfrac{n!}{(n-3)!}\\\\\\\Rightarrow \dfrac{2n(2n-1)(2n-2)(2n-3)!}{(2n-3)!}=100\times \dfrac{n(n-1)(n-2)(n-3)!}{(n-3!)}\\\\\\\Rightarrow 4(2n-1)=100\\\\\Rightarrow 2n-1=25\\\\\Rightarrow 2n=26\\\\\Rightarrow n= 13.$

Thus, the value of n for which the given equality holds is 13.

Answer 2

Answer:

n=13

Step-by-step explanation:

for explanation please see the attachment.

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