A school organization consists of 7 teachers, 7 parents and 8 students. A subcommittee of this group must be formed by choosing 4 teachers, 4 parents and 5 students. How many different subcommittees can be formed?
The number of ways to choosing 4 from 7 is \(\displaystyle \binom{7}{4}\)
and so on. So, we get:
\(\displaystyle \underbrace{\binom{7}{4}}_{\text{4 teachers from 7}}\cdot\overbrace{\binom{7}{4}}^{\text{4 parents from 7}}\cdot \underbrace{\binom{8}{5}}_{\text{5 students from 8}}\)
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