The three competitors in a race have to be randomly chosen from a group of four men and three women. How many different such trios contain at least one woman?  Pick one:
A) 10
B) 15
C) 16
D) 31
E) 46
The total number of ways to choose three runners 7C3 = 35   The number of trios with only males is 4C3 = 4   The number of trios which include at least one woman is 31.   The answer is 31.
<result>D</result>
The three competitors in a race have to be randomly chosen from a group of four men and three women. How many different such trios contain at least one woman?