How many arrangements can be made with 5 boys | vedclass

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Question

(A) There are two possible patterns for alternating arrangements: $1$. $B G B G B G B G B G$ $2$. $G B G B G B G B G B$ In the first pattern,$5$ boys

Vedclass · Accepted Answer

$2(5!)^2$

Vedclass · Answer

(A) There are two possible patterns for alternating arrangements: $1$. $B G B G B G B G B G$ $2$. $G B G B G B G B G B$ In the first pattern,$5$ boys can be arranged in $5!$ ways and $5$ girls can be arranged in $5!$ ways. Total arrangements for the first pattern $= 5! 	imes 5!$. Similarly,for the second pattern,the total arrangements $= 5! 	imes 5!$. Total number of arrangements $= 5! 	imes 5! + 5! 	imes 5! = 2 	imes (5!)^2$.

How many arrangements can be made with $5$ boys and $5$ girls in a row such that boys and girls alternate?

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