Of course other people must be either male or female. If the there are \(\displaystyle m\) total males & \(\displaystyle f\) total females in order for the males to be separated it has to be the case that \(\displaystyle 4\le m\le 7\). Given that the males are separated there must be at least \(\displaystyle m-1\) females.A committee of 14 people consists of 4 boys, 5 girls and 5 other people are arranged in a row. Given that the boys are separated, find the probability of the girls are not all together
Well Prof. Peterson my initial reaction was "are you serious "?I'll suppose that the "other people" are adults (or something else that isn't boys or girls), not that they are neither male nor female, or that they are just not known. The problem certainly could be clearer.
So you have some arrangement of BBBBGGGGGOOOOO. How many ways can they be arranged with no B's together? How many ways can they be arranged so that also GGGGG are all together? Where can you go from here?