A group consists of 8 boys and 5 girls. The n | vedclass

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(C) committee of $5$ is to be formed from $8$ boys and $5$ girls such that it consists of at least $2$ girls and at most $2$ boys.Since the committee

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$321$

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(C) committee of $5$ is to be formed from $8$ boys and $5$ girls such that it consists of at least $2$ girls and at most $2$ boys.Since the committee size is $5$,the possible combinations of (girls,boys) satisfying the conditions are:$1$. $5$ girls and $0$ boys: $\binom{5}{5} 	imes \binom{8}{0} = 1 	imes 1 = 1$$2$. $4$ girls and $1$ boy: $\binom{5}{4} 	imes \binom{8}{1} = 5 	imes 8 = 40$$3$. $3$ girls and $2$ boys: $\binom{5}{3} 	imes \binom{8}{2} = 10 	imes 28 = 280$Total number of ways = $1 + 40 + 280 = 321$.

$A$ group consists of $8$ boys and $5$ girls. The number of committees of $5$ persons that can be formed,if the committee consists of at least $2$ girls and at most $2$ boys,is:

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