SOLUTION: Out of 100 people in the US Senate, how many ways are there to select three Senate members to serve on a committee?

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Question 1181616: Out of 100 people in the US Senate, how many ways are there to select three Senate members to serve on a committee?


Answer by math_helper(2461) About Me  (Show Source):
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C(100,3) = 100!/((100-3)!3!) = (100*99*98)/(3*2) = 161700



This assumes the committee has a flat (equal) structure.  If someone is, for example, head of the committee then there are 3x as many possible committees (485100 = P(100,1)*C(99,2) )



If, additionally, you have a secretary (i.e. a committee head and secretary), then the number of possible committees is further increased by 2x  (970200 = P(100,3))