Question

find factorial of (n+2)!/(n+1)!
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Answer 1

Answer:

What is the factorial of 2n?

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By definition 2n! is the number of ways one can arrange 2n distinct objects in 2n places.

This can be calculated as

First place can be filled with 2n choices

Second place by 2n-1, third by 2n-2 and so on such that rth place will be filled by 2n-r+1 choices .

By product rule total number of ways to arrange these 2n objects i.e. 2n! is 2n(2n-1)(2n-2)…..3*2*1

One interesting result can be obtained by separating the odd and even terms in the above multiplication.

{2n(2n-2)(2n-4)….(2)}*{(2n-1)(2n-3)…..1}

Thus we have n even and n odd terms.

Take 2 common from all the even terms.

2n∗n(n−1)(n−2)....1∗(2n−1)(2n−3)…..1

= 2n∗n!∗ product of all odd terms upto 2n.

Step-by-step explanation:

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