The three competitors in a race have to be randomly chosen from a group of three men and four women. How many different such trios contain at least one woman?  Choose the correct choice from the following options.
A) 31 B) 34 C) 37 D) 40 E) 43
The total number of ways to choose three runners 7C3 = 35   The number of trios with only males is 3C3 = 1   The number of trios which include at least one woman is 34.   The answer is 34.
<result>B</result>
The three competitors in a race have to be randomly chosen from a group of three men and four women. How many different such trios contain at least one woman?