In how many ways can 5 boys and 5 girls stand | vedclass

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(C) First,arrange the $5$ boys in a row,which can be done in $5!$ ways.This creates $6$ possible gaps (including the ends) where the $5$ girls can be

Vedclass · Accepted Answer

$5! 	imes 6!$

Vedclass · Answer

(C) First,arrange the $5$ boys in a row,which can be done in $5!$ ways.This creates $6$ possible gaps (including the ends) where the $5$ girls can be placed to ensure no two girls are together: $\_ B_1 \_ B_2 \_ B_3 \_ B_4 \_ B_5 \_$.The number of ways to arrange $5$ girls in these $6$ gaps is given by $^6P_5 = \frac{6!}{(6-5)!} = 6!$.Therefore,the total number of arrangements is $5! 	imes 6!$.

In how many ways can $5$ boys and $5$ girls stand in a row so that no two girls may be together?

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