Number of Possible Committees Formed

[daneault23]

Homework Statement

A class consists of 50 students, 30 of which are Math majors. Five students are selected at random to form an advisory committee. How many possible committees contain at least 3 Math majors?

Homework Equations

n choose r = n!/((n-r)!r!) and we say that represents the number of possible combinations of n objects taken r at a time.

The Attempt at a Solution

Maybe I'm going about this the wrong way, but since we need at least 3 math majors that means we can have 3, 4, or 5 math majors in the committee. The way to have exactly 3 is (30 choose 3)*(20 choose 2). The way to have exactly 4 is (30 choose 4)*(20 choose 1), and the way to have exactly 5 is (30 choose 5)*(20 choose 0). So the number of possible committees that contain at least 3 math majors would be the sum of all of these possibilities, which equals 1,462,006.

 

[CAF123]

It is correct. Another way to see it is to find the number of possible committees without any restrictions on the number of Math majors and subtract from this the number of committees with 0, 1 and 2 Math majors.

A further question which might be asked later is to compute the probability that there are at least 3 Math majors in the committee of five.