Question

there are 15 students including john and mary, in the art club of a school a committee of 3 men consists of chairman secretary and treasurer is selected from the club. if john and mary cannot be both selected how many different committees can be formed ?


thank you:)

Answer 1

If the committee is really 3 men, then Mary can't be on it at all. I suspect you meant 3 people. In that case, if either John or Mary is on the committee, then there are only 13 other people to pick for the other two seats. That gives us

Committees with John: 13P2 = 156
Committees with Mary: 13P2 = 156
Committees with neither: 13P3 = 1716

Answer 2

Steve, I was thinking along these lines, can you find a flaw in this?


number of 3-person committees that can be formed from the 15 without any restrictions
= C(15,3) = 455

number of 3-person committees WITH BOTH John and Mary = C(13,1) = 13

so the number without both John and Mary
= 4550- 13
= 442

For each of these , the 3 jobs can be arranged in
3! or 6 ways

number of committees as described that can be formed
= 6(442) = 2652