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(D) Case $I$: No boy is included. Selecting $4$ girls from $6$ girls is ${}^6C_4 = 15$ ways. Selecting $1$ captain from the $4$ selected members is ${

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$380$

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(D) Case $I$: No boy is included. Selecting $4$ girls from $6$ girls is ${}^6C_4 = 15$ ways. Selecting $1$ captain from the $4$ selected members is ${}^4C_1 = 4$ ways. Total number of ways for Case $I = 15 	imes 4 = 60$.Case $II$: Exactly one boy is included. Selecting $3$ girls from $6$ girls and $1$ boy from $4$ boys is ${}^6C_3 	imes {}^4C_1 = 20 	imes 4 = 80$ ways. Selecting $1$ captain from the $4$ selected members is ${}^4C_1 = 4$ ways. Total number of ways for Case $II = 80 	imes 4 = 320$.Total number of ways $= 60 + 320 = 380$.

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