The number of ways in which 3 boys and 4 girl | vedclass

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(B) To ensure no two boys sit together,we first arrange the $4$ girls around a circular table. The number of ways to arrange $n$ objects in a circle i

Vedclass · Accepted Answer

$3! 	imes 4!$

Vedclass · Answer

(B) To ensure no two boys sit together,we first arrange the $4$ girls around a circular table. The number of ways to arrange $n$ objects in a circle is $(n-1)!$. Thus,$4$ girls can be seated in $(4-1)! = 3! = 6$ ways.After seating the girls,there are $4$ gaps created between them (as shown in the diagram). We need to place $3$ boys in these $4$ gaps such that no two boys are adjacent.The number of ways to choose and arrange $3$ boys in $4$ gaps is given by $^4P_3 = \frac{4!}{(4-3)!} = 4! = 24$ ways.Therefore,the total number of ways is $3! 	imes 4! = 6 	imes 24 = 144$.

The number of ways in which $3$ boys and $4$ girls can be seated around a circular table if no two boys sit together is:

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