A committee of 7 members is to be formed from | vedclass

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(B) We need to select $7$ members such that the number of boys $(B)$ is greater than the number of girls $(G)$. The total members are $B + G = 7$.Poss

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(B) We need to select $7$ members such that the number of boys $(B)$ is greater than the number of girls $(G)$. The total members are $B + G = 7$.Possible cases are:Case $1$: $4$ boys and $3$ girls. Number of ways = $\binom{6}{4} 	imes \binom{4}{3} = 15 	imes 4 = 60$.Case $2$: $5$ boys and $2$ girls. Number of ways = $\binom{6}{5} 	imes \binom{4}{2} = 6 	imes 6 = 36$.Case $3$: $6$ boys and $1$ girl. Number of ways = $\binom{6}{6} 	imes \binom{4}{1} = 1 	imes 4 = 4$.Total number of ways = $60 + 36 + 4 = 100$.

$A$ committee of $7$ members is to be formed from $6$ boys and $4$ girls such that the number of boys is greater than the number of girls. In how many ways can this be done?

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