Originally Posted by

**Ots**
2. How many ways can they be arranged if a particular boy and a particular girl have to be next to each other (paired). I would see this as a pair, two boys and three girls or six 'things' so probably 6!

I am not so sure about this. There is only a single way to actually arrange the boys/girls such that they are standing G B G B G B G. There are 4 spots for the girls, 4!. There are 3 spots for the guys, 3!. By the multiplication principle, the answer would be 4!3!. I just don't see how 6! limits the positions to boy girl boy girl...

Originally Posted by

**Ots**
3. If opposite sexes are at the ends. If the ends of G...B and B...G are considered to be the same, then 5! Basically, how many ways can five people be arranged in between a boy and a girl.

Again, I am not sure about this. If I think of this in cases. Case 1: a girl is in the first spot (there are 4 choices) and a boy is in the last spot (there are 3 choices). There are 5 people left to disperse among the middle spots, 5!. To the first case we have 4*3*5!. Case 2: a boy in the first spot (3 choices) and a girl in the last spot (4 choices). There are 5 people left for the middle, 5!. So the answer to this case is also 3*4*5!. By the addition principle we have 4*3*5! + 3*4*5!, or we can write this as 2*3*4*5!, or we can write this as 4!5!, but this last way seems a bit harder to actually understand what you're counting.