The three competitors on a race have to be randomly chosen from a group of five men and three women. How many different such trios contain at least one woman? Pick one.
A) 10  B) 15  C) 16  D) 30  E) 46
Total ways of choosing the runners randomly = (5+3)C3 = 8C3 = 56   Unwanted cases = team of 3 MAL46 runners = 5C3 = 10   Desired cases = 56 - 10= 
<gadget id="calculator">56 - 10</gadget>
<output>46</output>
46   Answer: Option 46
<result>E</result>
The three competitors on a race have to be randomly chosen from a group of five men and three women. How many different such trios contain at least one woman?