In a club there are 10 women and 7 men. A committee of 6 women and 4 men is to be chosen. How many different possibilities are there?

1 Answer
MathFact-orials.blogspot.com
May 14, 2017

7350 ways

Explanation:

We're choosing 6 women from a group of 10 and 4 men from a group of 7. We don't care in what order they are picked and so we'll use the combination formula, which is:

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

We'll multiply the results of the women and men together. And so we have:

#(C_(10,6))(C_(7,4))=((10!)/((6!)(10-6)!))((7!)/((4!)(7-4)!))=>#

#=> ((10!)/((6!)(4!)))((7!)/((4!)(3!)))=(10!7!)/(6!4!4!3!)=>#

#=> (10xxcancel9^3xxcancel8xx7xxcancel(6!)xx7xxcancel6xx5xxcancel(4!))/(cancel(6!)xxcancel(4!)xxcancel4xxcancel3xxcancel2xxcancel(3xx2))=>#

#=> 10xx3xx7xx7xx5=7350# ways

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