In how many ways can 5 girls and 3 boys be se | vedclass

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(A) First,arrange the $5$ girls in a row. This can be done in $5!$ ways.There are $6$ possible gaps created between and at the ends of the girls,repre

Vedclass · Accepted Answer

$14400$

Vedclass · Answer

(A) First,arrange the $5$ girls in a row. This can be done in $5!$ ways.There are $6$ possible gaps created between and at the ends of the girls,represented by $	imes$:$	imes G_1 	imes G_2 	imes G_3 	imes G_4 	imes G_5 	imes$To ensure no two boys are together,we must place the $3$ boys in these $6$ available gaps.This can be done in $^6P_3$ ways.Total number of ways $= 5! 	imes ^6P_3 = 120 	imes (6 	imes 5 	imes 4) = 120 	imes 120 = 14400$.

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

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