Question

There are 20 persons including two brothers. In how many ways can they be arranged on a round table if:
The two brothers are always separated.

Answer 1

In the 2nd case in between 18 gaps on the round table between 18 persons we have to arrange these two brothers and it can be done in ${}^{18}{P}_2$ ways. Hence the required number in this case will be
${}^{18}{P}_2$ (17) ! = 18 $\cdot$ 17 $\cdot$ (17) !=17 (18)!