(D) Case $I$: No boy is included.Selecting $4$ girls from $6$ girls $= {}^{6}C_{4} = 15$.Selecting $1$ leader from the $4$ selected members $= {}^{4}C

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(D) Case $I$: No boy is included.Selecting $4$ girls from $6$ girls $= {}^{6}C_{4} = 15$.Selecting $1$ leader from the $4$ selected members $= {}^{4}C_{1} = 4$.Total ways for Case $I = 15 \times 4 = 60$.Case $II$: Exactly one boy is included.Selecting $3$ girls from $6$ girls and $1$ boy from $4$ boys $= {}^{6}C_{3} \times {}^{4}C_{1} = 20 \times 4 = 80$.Selecting $1$ leader from the $4$ selected members $= {}^{4}C_{1} = 4$.Total ways for Case $II = 80 \times 4 = 320$.Therefore,the total number of ways $= 60 + 320 = 380$.

Class 11 Mathematics Permutation and Combination Mix Examples-Permutation and Combination

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

MHT CET 2023 All MHT CET

A
$140$
B
$320$
C
$76$
D
$380$

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

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