The number of ways of arranging 8 boys and 8 | vedclass

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(D) There are two possible cases for sitting alternately:Case $1$: The arrangement starts with a boy: $B G B G B G B G B G B G B G B G$.The number of

Vedclass · Accepted Answer

$2!(8!)^2$

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(D) There are two possible cases for sitting alternately:Case $1$: The arrangement starts with a boy: $B G B G B G B G B G B G B G B G$.The number of ways to arrange $8$ boys in $8$ positions is $8!$ and $8$ girls in $8$ positions is $8!$. So,$8! 	imes 8!$ ways.Case $2$: The arrangement starts with a girl: $G B G B G B G B G B G B G B G B$.The number of ways to arrange $8$ girls in $8$ positions is $8!$ and $8$ boys in $8$ positions is $8!$. So,$8! 	imes 8!$ ways.Total number of arrangements $= 8! 	imes 8! + 8! 	imes 8! = 2 	imes (8!)^2 = 2!(8!)^2$.

The number of ways of arranging $8$ boys and $8$ girls in a row so that boys and girls sit alternately is

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