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

1 Answer

MathFact-orials.blogspot.com

May 6, 2017

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#

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