1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Number of Possible Committees Formed

  1. Dec 9, 2013 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant 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.

    3. 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.
     
  2. jcsd
  3. Dec 9, 2013 #2

    CAF123

    User Avatar
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted