The number of ways,in which 5 girls and 7 boy | vedclass

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(A) First,arrange the $7$ boys in a circle. The number of ways to arrange $7$ boys in a circle is $(7-1)! = 6!$.There are $7$ gaps created between the

Vedclass · Accepted Answer

$126(5!)^2$

Vedclass · Answer

(A) First,arrange the $7$ boys in a circle. The number of ways to arrange $7$ boys in a circle is $(7-1)! = 6!$.There are $7$ gaps created between the boys in the circular arrangement.We need to place $5$ girls in these $7$ gaps such that no two girls sit together. The number of ways to choose $5$ gaps out of $7$ is $^7C_5$.The number of ways to arrange $5$ girls in the chosen $5$ gaps is $5!$.Total number of ways = $6! 	imes ^7C_5 	imes 5!$.$= 720 	imes 21 	imes 120$.$= 720 	imes 21 	imes 120 = 1,814,400$.Calculating the expression in option $A$: $126 	imes (120)^2 = 126 	imes 14,400 = 1,814,400$.Thus,the correct option is $A$.

The number of ways,in which $5$ girls and $7$ boys can be seated at a round table so that no two girls sit together,is

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