Science

Math

Humanities

... and beyond

Socratic Meta
Featured Answers

Topics

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#

Related questions

See all questions in Combinations and Permutations

Impact of this question

5951 views around the world

You can reuse this answer
Creative Commons License