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At a high school, a committee is created to organize fun activities. A committee of 8...

At a high school, a committee is created to organize fun activities. A committee of 8 is to be chosen from the following groups: 5 teachers, 14 Senior students and 11 Junior students. In how many ways can this be done if:

a) a representative from each group must be on the committee

b) the committee must have at most 2 junior students

c)Bill, Kathy and Mary, three of the senior students, have decided that either all three will serve on the committee or none of them will serve on the committee?

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