20 persons are to be seated around a circular table. Out of these 20 , 2 of them are brothers then number of arrangements in which there will be at least three persons between the brothers is.?
SO here's what I tried. First fix the postions of the two brothers then put the rest of the 18 people in the remaining places.
So there are 7 such cases.: 3,15 4,16 5,13 6,12 7,11 8,10 9,9.
So for example the first 3-15 case I first selected 3 out of 18 that is 18c3 and multiplied it by 3! and 15! to get the answer as 18! . The same results goes for all the other cases so the answer now is 7 * 18! . But the brothers themselves can be arranged in 2! ways .
So the answer im getting is 14*18!. The actual answer is 13*18!. SO what am I doing wrong?