The music class consists of 4 girls and 5 boys. How many ways can a group of 3 be formed if it has to include at least one boy?  Pick one.
A) 80  B) 158  C) 161  D) 165  E) 172
Reverse combinatorics approach is preferred method on this one   Note that at least 1 boy gives clue to using this method   80ll combinations - four girls = answer   80ll combinations is 9C3 = 84   80ll girls 4C3 = 4   So our answer is   84-4= 
<gadget id="calculator">  84-4</gadget>
<output>80</output>
80   Hence, answer is (80)
<result>A</result>
The music class consists of 4 girls and 5 boys. How many ways can a group of 3 be formed if it has to include at least one boy?