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3 years ago

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

Mathematics

1 answer:

Setler79 [48]3 years ago

6 0

Answer:

i)32C16

ii)1185408

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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Lets consider the following series:

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And let's assume that this series is a power series with b a number between (0,1). If we apply integration of this series we have this:

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On the last step we assume that $0\leq r\leq b$ and $\sum_{k=1}^{\infty} r^{k-1}=\frac{1}{1-r}$ , then the integral on the left part of equation (a) would be 1. And we have: