The number of ways in which 5 boys and 4 girl | vedclass

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(B) First,arrange the $5$ boys around a circular table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. So,the number of ways to ar

Vedclass · Accepted Answer

$4! 	imes 5!$

Vedclass · Answer

(B) First,arrange the $5$ boys around a circular table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. So,the number of ways to arrange $5$ boys is $(5-1)! = 4! = 24$.
There are $5$ spaces created between the $5$ boys where the $4$ girls can sit to ensure no two girls sit together.
The number of ways to arrange $4$ girls in these $5$ spaces is given by $P(5, 4) = \frac{5!}{(5-4)!} = \frac{120}{1} = 120$.
Therefore,the total number of ways is $4! 	imes 120 = 24 	imes 120 = 2880$.
This is equivalent to $4! 	imes 5!$.

The number of ways in which $5$ boys and $4$ girls can sit around a circular table such that no two girls sit together is:

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