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

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(C) Step $1$: Arrange the $5$ boys in a row. The number of ways to arrange $5$ boys is $5!$.Step $2$: To ensure no two girls sit together,we place the

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$^6P_3 	imes 5!$

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(C) Step $1$: Arrange the $5$ boys in a row. The number of ways to arrange $5$ boys is $5!$.Step $2$: To ensure no two girls sit together,we place the girls in the gaps created by the boys. With $5$ boys,there are $6$ possible gaps (including the ends) where the $3$ girls can be seated.Step $3$: The number of ways to choose and arrange $3$ girls in these $6$ gaps is given by the permutation formula $^6P_3$.Step $4$: The total number of ways is the product of the arrangements of boys and the arrangements of girls: $5! 	imes ^6P_3$.

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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