A group of 5 men and 5 women stand in line to have their photo taken.
How many ways can they stand in line if no two men and no two women stand together?
My method: _M_M_M_M_M_
Male * Female = 5P5 * 6P5 = 86400
Correct Answer = 5! * 5! * 2 = 28800
I don't understand why I got it wrong, can anyone help please?
If you distiguish only by man and woman, then they can be arranged: $$m-w-m-w-m-w-m-w-m-w$$ and $$w-m-w-m-w-m-w-m-w-m$$
If you distinguish the womans, there are $5!$ possibilities. The same for men.