Question

A committee consisting of 2 faculty members and 3 students is to be formed. Every committee position has the same duties and voting rights. There are 6 faculty members and 15 students eligible to serve on the committee. In how many ways can the committee be formed?

Answer 1

Answer

this is a combination problem where order of selection does not matter

For faculty members, we have n = 6 and r = 2

and for students, we have n = 15 and r = 3

using combination formula C(n,r) = n!/((n-r)!*r!)

setting the values

Required number of committees = C(6,2)*C(15,3)

= {6!/((6-2)!*2!}*{15!/((15-3)!*3!}

= 15*455

= 6825 ways