In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?  Pick one
A) 63 B) 67 C) 70 D) 74 E) 80
We need to select 5 men from 7 men and 2 women from 3 women.   Number of ways to do this   = 7C5 × 3C2   = 7C2 × 3C1 [∵ nCr = nC(n-r)]   =   7   ×   6   2   ×   1   ×   3   =   21   ×   3   =   63   63)
<result>A</result>
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?