SOLUTION: A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 7 sophomores, 8 juniors, and 9 seniors are eligible to be on the commit

Algebra ->  Inequalities -> SOLUTION: A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 7 sophomores, 8 juniors, and 9 seniors are eligible to be on the commit      Log On


   

Question 1153264: A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 7 sophomores, 8 juniors, and 9 seniors are eligible to be on the committee, in how many ways can the committee be chosen?
Answer by greenestamps(13200) About Me  (Show Source):
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Straightforward application of two basic principles: (1) "n choose r" and (2) fundamental counting principle.

Choose 2 of the 6 eligible freshmen: "6 choose 2" = C(6,2) = 15
Choose 3 of the 7 eligible sophomores: 7 choose 3 = 35
Choose 4 of the 8 eligible juniors: 8 choose 4 = 70
Choose 5 of the 9 eligible seniors: 9 choose 5 = 126

All together: 15*35*70*126 = 4,630,500 ways