In how many ways can a team of 3 boys and 3 g | vedclass

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Question

(A) team of $3$ boys and $3$ girls is to be selected from $5$ boys and $4$ girls.$3$ boys can be selected from $5$ boys in $^{5}C_{3}$ ways.$3$ girls

Vedclass · Accepted Answer

$40$

Vedclass · Answer

(A) team of $3$ boys and $3$ girls is to be selected from $5$ boys and $4$ girls.$3$ boys can be selected from $5$ boys in $^{5}C_{3}$ ways.$3$ girls can be selected from $4$ girls in $^{4}C_{3}$ ways.Therefore,by the multiplication principle,the number of ways in which a team of $3$ boys and $3$ girls can be selected is given by:$^{5}C_{3} 	imes ^{4}C_{3} = \frac{5!}{3!2!} 	imes \frac{4!}{3!1!}$$= \frac{5 	imes 4}{2 	imes 1} 	imes \frac{4}{1}$$= 10 	imes 4 = 40$ ways.

In how many ways can a team of $3$ boys and $3$ girls be selected from $5$ boys and $4$ girls?

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