Out of 6 boys and 4 girls,a group of 7 is to | vedclass

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(C) To form a group of $7$ with a majority of boys,we consider the following cases:Case $1$: $6$ boys and $1$ girl. The number of ways is $^6C_6 	ime

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(C) To form a group of $7$ with a majority of boys,we consider the following cases:Case $1$: $6$ boys and $1$ girl. The number of ways is $^6C_6 	imes ^4C_1 = 1 	imes 4 = 4$.Case $2$: $5$ boys and $2$ girls. The number of ways is $^6C_5 	imes ^4C_2 = 6 	imes 6 = 36$.Case $3$: $4$ boys and $3$ girls. The number of ways is $^6C_4 	imes ^4C_3 = 15 	imes 4 = 60$.Total number of ways = $4 + 36 + 60 = 100$.

Out of $6$ boys and $4$ girls,a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys?

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