In how many ways can 5 boys and 3 girls sit i | vedclass

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(C) First,arrange the $5$ boys in a row. They can be arranged in $5!$ ways.After arranging the boys,we create gaps between them to ensure no two girls

Vedclass · Accepted Answer

$^6P_3 	imes 5!$

Vedclass · Answer

(C) First,arrange the $5$ boys in a row. They can be arranged in $5!$ ways.After arranging the boys,we create gaps between them to ensure no two girls are together.The arrangement of $5$ boys creates $6$ possible gaps (including the ends): $\_ B_1 \_ B_2 \_ B_3 \_ B_4 \_ B_5 \_$.We have $3$ girls to be placed in these $6$ gaps.The number of ways to choose and arrange $3$ girls in $6$ gaps is given by $^6P_3$.Therefore,the total number of ways is $^6P_3 	imes 5!$.

In how many ways can $5$ boys and $3$ girls sit in a row so that no two girls are together?

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