Interesting GMAT Questions – m25q02 | B-School Admissions Formula

How many integers are divisible by 3 between $10!$ and $10! + 20$ inclusive?

* 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?

* 36
* 60
* 72
* 80
* 100

First, consider an unconstrained version of the question: how many committees of 3 are possible? The answer is $C_{10}^3 = \frac{10!}{(7!3!)} = 120$ . Now subtract the number of committees that consist entirely of students i.e. $C_{6}^3 = \frac{6!}{(3!3!)} = 20$ . The final answer is $C_{10}^3 - C_6^3 = 120 - 20 = 100$ .