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
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
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