A group consists of 4 girls and 7 boys. In ho | vedclass

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(A) The total number of members to be selected is $5$. The team must contain at least one boy and one girl.The possible compositions of the team are:$

Vedclass · Accepted Answer

$441$

Vedclass · Answer

(A) The total number of members to be selected is $5$. The team must contain at least one boy and one girl.The possible compositions of the team are:$(a)$ $1$ boy and $4$ girls: $^{7}C_{1} 	imes ^{4}C_{4} = 7 	imes 1 = 7$ ways.$(b)$ $2$ boys and $3$ girls: $^{7}C_{2} 	imes ^{4}C_{3} = 21 	imes 4 = 84$ ways.$(c)$ $3$ boys and $2$ girls: $^{7}C_{3} 	imes ^{4}C_{2} = 35 	imes 6 = 210$ ways.$(d)$ $4$ boys and $1$ girl: $^{7}C_{4} 	imes ^{4}C_{1} = 35 	imes 4 = 140$ ways.Total number of ways = $7 + 84 + 210 + 140 = 441$.

$A$ group consists of $4$ girls and $7$ boys. In how many ways can a team of $5$ members be selected if the team has at least one boy and one girl?

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