SOLUTION: Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed. In how many ways this be done if one particular physicist mus

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Question 870213: Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed. In how many ways this be done if one particular physicist must be on the committee?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If one particular physicist must be on the committee, then you really only have 3-1=2 slots left for physicists. So you'll have 7-1 = 6 physicists left to pick from.


There are 5 nCr 2 = 10 ways to pick 2 mathematicians (from a pool of 5)


There are 6 nCr 2 = 15 ways to pick 2 physicists (from a pool of 6)


Side Note: I'm using the combination formula to compute nCr


So there are 10*15 = 150 ways to form a 4 person committee (2 mathematicians and 2 physicists)


By extension, there are also 150 ways to form a 5 person committee (2 mathematicians and 3 physicists) with one physicist slot taken. This is because that particular physicist who must be on the committee doesn't change the count (you'll have 1*150 = 150)