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4 professors and 6 students are being considered for

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4 professors and 6 students are being considered for [#permalink] New post 06 Jun 2007, 21:34
4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. In how many ways can this committee be formed if it has to include at least 1 professor ?
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 [#permalink] New post 06 Jun 2007, 22:02
Since a committee containing prof. A& B is similar to committee containing prof. B&A so it means that order doesn't matter and therefore it is a combinations problem.
Now, this question has three possible committe compositions, 1) with 1 prof and 2 studets, 2) with 2 prof and 1 students and 3) with 3 prof. and no students in the committee.
SO working the maths now
1 prof from 4 can be chosen in 4C1 wasy and 2 students from 6 studnets can be chosen in 6C2 ways. Similarly setting up maths for other two combinations, we get
(4C1*6C2)+(4C2*6C1)+(4C3)
=(4!/3!*6!/2!*4!)+(4!/2!*2!*6!/5!)+(4!/3!)
=(4*15)+(6*6)+(4)
=60+36+4
=100 Ans
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  [#permalink] 06 Jun 2007, 22:02
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