The number of ways in which 5 boys and 3 girl | vedclass

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Question

(A) To ensure each girl is between two boys,we first arrange the $5$ boys in a row. The number of ways to arrange $5$ boys is $5! = 120$.Let the boys

Vedclass · Accepted Answer

$2880$

Vedclass · Answer

(A) To ensure each girl is between two boys,we first arrange the $5$ boys in a row. The number of ways to arrange $5$ boys is $5! = 120$.Let the boys be represented by $B$. The arrangement looks like: $\_ B \_ B \_ B \_ B \_ B \_$.There are $4$ possible spaces between the $5$ boys where the $3$ girls can be seated to satisfy the condition that each girl is between two boys.The number of ways to choose and arrange $3$ girls in these $4$ spaces is given by $^4P_3 = 4 	imes 3 	imes 2 = 24$.Therefore,the total number of ways is $5! 	imes ^4P_3 = 120 	imes 24 = 2880$.

The number of ways in which $5$ boys and $3$ girls can be seated in a row so that each girl is between two boys is:

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