A debate club consists of 6 girls and 4 boys. | vedclass

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Question

(A) Case $1$: $0$ boys are included.Selecting $4$ girls from $6$ girls is given by ${}^6C_4 = 15$.Selecting $1$ captain from the $4$ selected members

Vedclass · Accepted Answer

$380$

Vedclass · Answer

(A) Case $1$: $0$ boys are included.Selecting $4$ girls from $6$ girls is given by ${}^6C_4 = 15$.Selecting $1$ captain from the $4$ selected members is given by ${}^4C_1 = 4$.Total ways for Case $1 = 15 	imes 4 = 60$.Case $2$: $1$ boy is included.Selecting $3$ girls from $6$ and $1$ boy from $4$ is given by ${}^6C_3 	imes {}^4C_1 = 20 	imes 4 = 80$.Selecting $1$ captain from the $4$ selected members is given by ${}^4C_1 = 4$.Total ways for Case $2 = 80 	imes 4 = 320$.Total number of ways $= 60 + 320 = 380$.

$A$ debate club consists of $6$ girls and $4$ boys. $A$ team of $4$ members is to be selected from this club,including the selection of a captain (from among these $4$ members) for the team. If the team has to include at most one boy,then the number of ways of selecting the team is

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