A committee is formed from a set of 17 professors and 40 students. How many ways

ID: 3141807 • Letter: A

Question

A committee is formed from a set of 17 professors and 40 students. How many ways are there to form the committee if:

4.a. The committee consists of 4 professors and 4 students?

4.b. The committee can be of any non-zero size, but must have equal numbers of professors and students?

4.c. The committee has 6 members and one must be Prof. Li?

4.d. The committee has 10 members and at least 4 are professors?

4.e. The committee has 20 members, and both Prof Li and student Jim cannot both be on the committee?

USINED Excel.

a. The committee consists of 4 professors and 4 students?

=17C4*40C4= =COMBIN(17,4)*COMBIN(40,4)=

b. The committee can be of any non-zero size, but must have equal numbers of professors and students?

=17C1*40C1 + 17C2*40C2 +17C3*40C3 +.....+17C17*40C17

Excel formula:

c. The committee has 6 members and one must be Prof. Li?

Now we have 16 professors since 1 is already selected and have to choose 5 members from total of 16+40:

=56C5 =

d. The committee has 10 members and at least 4 are professors?

calculations:

e. The committee has 20 members, and both Prof Li and student Jim cannot both be on the committee?

Now we have to choose 20 members from rest of 16 professors and 39 students (total=55):

= 55C20 =

eXcel: =COMBIN(55,20)

Note: In such combinations order doesn't matter.

217508200

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