Question

Which of the following is not equivalent to 15!/10!5!

P(15, 10)

C(15, 10)

C(15, 5)

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Answer 1

Answer:

P(15, 10)

Step-by-step explanation:

By definition;

$nC_r=\binom{n}{r}=\frac{n!}{(n-r)!r!}$

and

$nP_r=\binom{n}{r}=\frac{n!}{(n-r)!}$

This implies that;

$15P_{10}=\binom{15}{10}=\frac{15!}{(15-10)!}=\frac{15!}{5!}$

$15C_{10}=\binom{15}{10}=\frac{15!}{(15-10)!10!}=\frac{15!}{5!10!}$

$15C_{5}=\binom{15}{5}=\frac{15!}{(15-5)!5!}=\frac{15!}{5!10!}$