In how many ways can a committee of three men and three women be formed from a group of eight men and seven women

Explanation:

Order doesn't matter when it comes to committees without rankings. Each person on the committee is of equal rank to anyone else. This means we'll use a combination instead of a permutation.

We have 8 men and 3 seats to fill for the men. Plug n = 8 and r = 3 into the nCr combination formula

n C r = (n!)/(r!(n-r)!)

8 C 3 = (8!)/(3!*(8-3)!)

8 C 3 = (8!)/(3!*5!)

8 C 3 = (8*7*6*5*4*3*2*1)/((3*2*1)*(5*4*3*2*1))

8 C 3 = (40320)/((6)*(120))

8 C 3 = (40320)/(720)

8 C 3 = 56

This means there are 56 ways to select the three men from a pool of eight.

Through similar steps, you should plug n = 7 and r = 3 into the nCr combination formula to get 7 C 3 = 35. This means there are 35 ways to pick the three women from a pool of seven.

Overall, there are 56*35 = 1960 ways to select the entire committee of 3 men and 3 women (from a pool of 8 men and 7 women).

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