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.
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Solution
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 18P2 ways. Hence the required number in this case will be 18P2 (17) ! = 18 ⋅ 17 ⋅ (17) !=17 (18)!