Question

7 freshmen, 9 sophomores, 8 juniors, and 8 seniors are eligible to be on a committee.

In how many ways can a dance committee of 16 students be chosen?


In how many ways can a dance committee be chosen if it is to consist of 5 freshmen, 2 sophomores, 6 juniors, and 3 seniors.

Answer 1

i)32C16

ii)1185408

Step-by-step explanation:

i)Total number of selected/eligible is 7+9+8+8=32

Total ways of selecting dance committee of 16 is

32C16

ii)Total ways of selecting 3 seniors from 8 is 8C3

and Total ways of selecting 6 juniors from 8 is 8C6

ways of selecting 2 sopho from 9 is 9C2

ways of selecting 5 freshman from 7 is 7C5

now, total way of selection come to be

8C3×8C6×9C2×7C5

=56×28×36×21

=1185408

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