How many integers are divisible by 3 between and inclusive?

(C) 2008 GMAT Club – m25#2

* 6
* 7
* 8
* 9
* 10

4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 1 professor, how many ways can this committee be formed?

(C) 2008 GMAT Club – m25#3

* 36
* 60
* 72
* 80
* 100

First, consider an unconstrained version of the question: how many committees of 3 are possible? The answer is . Now subtract the number of committees that consist entirely of students i.e. . The final answer is .

The correct answer is E.