Question

How do you evaluate `""_8C_5 * _7C_3`?

Answer 1

1960

Explanation:

The combinations general formula is:

`C_(n,k)=(n!)/((k!)(n-k)!)` with `n="population", k="picks"`

So we can write:

`C_(8,5)xxC_(7,3)=(8!)/((5!)(8-5)!)xx(7!)/((3!)(7-3)!)=((8!)(7!))/((5!)(3!)(3!)(4!))`

Let's evaluate it:

`=((8xx7xxcancel(6xx5!))(7xxcancel6xx5xxcancel(4!)))/cancel((5!)(4!)(6)(6))=8xx7xx7xx5=1960`