Six boys can be placed in 7 places in 7 C 1 ways.
Probability of no 2 boys sitting together is 2/7.
please correct me if I am wrong.
If there are six boys and six girls, then we can arrange them in a row in 12! ways.
If no two boys sit together, then either:
- the boys sit in places 1, 3, ..., 11 (and the girls in places 2, 4, ..., 12); or
- the boys sit in places 2, 4, ..., 12 (and the girls in places 1, 3, ..., 11)
Each of these arrangements can be done in 6! x 6! different ways. So the probability that one of these occurs is