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

P(15, 10)

Explanation:

By definition;

`nC_r=\binom{n}{r}=(n!)/((n-r)!r!)`

and

`nP_r=\binom{n}{r}=(n!)/((n-r)!)`

This implies that;

`15P_(10)=\binom{15}{10}=(15!)/((15-10)!)=(15!)/(5!)`

`15C_(10)=\binom{15}{10}=(15!)/((15-10)!10!)=(15!)/(5!10!)`

`15C_(5)=\binom{15}{5}=(15!)/((15-5)!5!)=(15!)/(5!10!)`