SOLUTION: In how many ways can a committee consisting of 3 men and 7 women be selected from a group consisting of 20 men and 15 women?

Question 1204282: In how many ways can a committee consisting of 3 men and 7 women be selected from a group consisting of 20 men and 15 women?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

n = 20 men
r = 3 selections
Order doesn't matter on a committee since none of the seats are labeled (eg: chairman, president, VP, etc), so we use the nCr combination formula.
n C r = (n!)/(r!(n-r)!)
20 C 3 = (20!)/(3!*(20-3)!)
20 C 3 = (20!)/(3!*17!)
20 C 3 = (20*19*18*17!)/(3!*17!)
20 C 3 = (20*19*18)/(3!)
20 C 3 = (20*19*18)/(3*2*1)
20 C 3 = 6840/6
20 C 3 = 1140
There are 1140 ways to select the 3 men from a candidate pool of 20 men.

Similar calculations will lead us to 15C7 = 6435 ways to select 7 women from a candidate pool of 15 women.

Ultimately there are 1140*6435 = 7,335,900 ways to form this committee.

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