SOLUTION: In how many ways can a committee consisting of 4 faculty members and 5 students be formed if there are 11 faculty members and 15 students eligible to serve on the committee?

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Question 1081006: In how many ways can a committee consisting of 4 faculty members and 5 students be formed if there are 11 faculty members and 15 students eligible to serve on the committee?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
For the faculty members:
C( 11, 4 )
For the students:
C( 15, 5 )
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Each of the groups of 4 faculty members
are able to combine with a group of
5 student members in the following way:
C( 11,4 ) x C( 15, 5 )
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C( 11, 4 ) = +11%21+%2F+%28+4%21%2A%28+11+-+4+%29%21+%29+
C( 11, 4 ) = +11%21+%2F+%28+4%21%2A7%21+%29+
C( 11,4 ) = +%28+8%2A9%2A10%2A11+%29+%2F+%28+4%2A3%2A2%2A1+%29+
C( 11,4 ) = +7920+%2F+24+
C( 11,4 ) = +330+
and
C( 15,5 ) = +15%21+%2F+%28+5%21%2A%28+15+-+5+%29%21+%29+
C( 15,5 ) = +15%21+%2F+%28+5%21%2A10%21+%29+
C( 15,5 ) = +%28+11%2A12%2A13%2A14%2A15+%29+%2F+%28+5%2A4%2A3%2A2%2A1+%29+
C( 15,5 ) = +360360+%2F+120+
C( 15,5 ) = +3003+
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C( 11,4 ) x C( 15, 5 ) = +330%2A3003+
C( 11,4 ) x C( 15, 5 ) = +990990+
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There are 990,990 ways to form a committee
Definitely get a 2nd opinion ( if needed ) on this.