Permutations

Question

In how many ways can a committee consisting of
4
faculty members and
5
students be formed if there are
7
faculty members and
13
students eligible to serve on the committee?

Answer 1

Hi April,

This is a neat problem, but I don't think it is a "Permutation" problem since the order that the members are chosen is not important.  

 

You would use combinations to find out how many ways can 4 faculty be chosen from 7 choices.  

This could be written as C(7,4) and equals 7!/(3!4!) = 35

 

Similarly, choosing 5 students from a group of 13 could be written as C(13,5) and equals 13!/5!8! = 1287

 

Since there are 35 ways to choose the faculty and 1287 ways to choose the students, the total number of ways to form the committee is simply 35 x 1287 = 45,045

 

Hope this helps.