sumana wrote:

A university needs to select a nine-member committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 10 members , the student advisory board consists of 8 members and 6 students hold membership in both organizations , how many different committee are possible.

A. 72

B. 110

C. 220

D. 720

E. 1096

The number of students who belong either to the student government or to the student advisory board or both is:

Total = # Government + # Advisory - # Both + # Neither

10 + 8 - 6 + 0 = 12 students.

So the number of ways to select the 9-member committee out of 12 possible candidates is 12C9:

12!/[(12-9)! x 9!]

12!/(3! x 9!) = (12 x 11 x 10)/3! = (12 x 11 x 10)/(3 x 2) = 2 x 11 x 10 = 220

Answer: C

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