Question

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?

Answer 1

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