SOLUTION: MAT 145: Topics In Contemporary Math Permutations and Combinations 4. SUNY Schenectady has 55 full-time faculty members. How many 5-member hiring committees can be formed to

Question 1190906: MAT 145: Topics In Contemporary Math
Permutations and Combinations
4. SUNY Schenectady has 55 full-time faculty members. How many 5-member hiring
committees can be formed to interview candidates to replace a retiring professor?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
this is 55C5=3,478,761 different committees
there are ultimately going to be 5 on the committee and 50 not.
There are 55*54*53*52*51*50! ways to choose the first
There are 5*4*3*2*1 ways to choose the 5 people on the committee
There are 50*49*48*47*46*....ways to choose the 50 people NOT on the committee
it is 55*54*53*52*51*50!/50!*120, the 120 being 5!, or 5*4*3*2*1
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