The number of ways a committee of 8 members c | vedclass

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(A) We need to form a committee of $8$ members from $10$ men and $8$ women such that there are at most $5$ men and at least $5$ women. Since the total

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$8061$

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(A) We need to form a committee of $8$ members from $10$ men and $8$ women such that there are at most $5$ men and at least $5$ women. Since the total number of members is $8$,the possible combinations of (women,men) are: $(5, 3), (6, 2), (7, 1), (8, 0)$. The number of ways is given by: $\sum_{k=5}^{8} {}^{8}C_{k} 	imes {}^{10}C_{8-k}$ $= {}^{8}C_{5} 	imes {}^{10}C_{3} + {}^{8}C_{6} 	imes {}^{10}C_{2} + {}^{8}C_{7} 	imes {}^{10}C_{1} + {}^{8}C_{8} 	imes {}^{10}C_{0}$ $= (56 	imes 120) + (28 	imes 45) + (8 	imes 10) + (1 	imes 1)$ $= 6720 + 1260 + 80 + 1 = 8061$.

The number of ways a committee of $8$ members can be formed from a group of $10$ men and $8$ women such that the committee contains at most $5$ men and at least $5$ women is:

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