Question

Find the number of ways in which $5$ boys and $4$ girls can be arrange on a circular table such that no two girls sit together and two particular boys are always together.

Answer 1

$2$ particular boys always together.take them as a unit.Now 1 unit +3 Boys can be count as 4 persons

$4$ boy can be arranged in $(4-1)!$

$=3!$ ways

Those two boys can be interchanged

$=6\times 2=12$

$4$ girls in $4$ places$=4!$ ways

$12\times 4\times 3\times 2=12\times 12\times 2=144\times 2$

$=288$ ways