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

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Answer 1 · 2017-05-06T11:15:28

1960

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:

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

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