Question 1204282
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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 = <font color=red size=4>7,335,900</font> ways to form this committee.
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