The Department of Economics at X University consists of 44 f

The Department of Economics at X University consists of 44 faculty members.

(A) In how many ways can a committee of 6 faculty members be formed?

(B) The committee must have a chair, vice-chair, and secretary. From a given group of 6 faculty members, how many different assignments of these positions can be made?

(C) Three faculty committees are to be formed: the admissions committee (with 11 members), the fellowship committee (12 members), and the search committee (15 members). In how many ways can the faculty members be assigned to the three different committees, if no one has to serve on more than one committee?

Solution

a)

Order does not matter here. Hence, there are

44C6 = 7059052 ways [answer]

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b)

Here, order matters, as this is position.

Hence, there are

6P3 = 120 [answer]

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c)

There are 44C11 = 7669339132 ways to choose the admissions committee.

There are 33 left.

There are 33C12 = 354817320 ways to choose fellowship committee.

There are 21 left.

There are 21C15 = 54264 ways to choose search committee.

Thus, multiplying these, there are a total of 1.47664*10^23 ways. [ANSWER]