Permutations Practice Test 1

Question : 11 of 40

Marks: +1, -0

The product of r consecutive positive integers, divided by r!, is:

Solution:

Consider r consecutive positive integers n + 1, ..., n + r – 1, n + r
Then

{(n+1)...(n+r)}/r!

={n!(n+1)...(n+r)}/{n!r!}

= ^{n + r}C_r

, which is a positive integer.

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