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(A) There are $5$ benches,each with $2$ seats,making a total of $10$ seats in a row.To ensure no two boys or no two girls sit together,the genders mus

Vedclass · Accepted Answer

$28800$

Vedclass · Answer

(A) There are $5$ benches,each with $2$ seats,making a total of $10$ seats in a row.To ensure no two boys or no two girls sit together,the genders must alternate: $B G B G B G B G B G$ or $G B G B G B G B G B$.Case $1$: The pattern is $B G B G B G B G B G$.The $5$ boys can be arranged in $5!$ ways and the $5$ girls can be arranged in $5!$ ways.Number of arrangements $= 5! 	imes 5! = 120 	imes 120 = 14400$.Case $2$: The pattern is $G B G B G B G B G B$.The $5$ girls can be arranged in $5!$ ways and the $5$ boys can be arranged in $5!$ ways.Number of arrangements $= 5! 	imes 5! = 120 	imes 120 = 14400$.Total arrangements $= 14400 + 14400 = 28800$.

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