Answer:
As there are 5 men and 4 women and they have to arrange a line, they should be positiones like this to be alternated:
MAN - WOMAN- MAN - WOMAN - MAN - WOMAN - MAN - WOMAN - MAN
In the first position they can be put 5 mans, but in the third, 4, as one has been put before, and in the fifth 3, and in the seventh 2 and in the ninth one.
In the second position they can be put 4 women, then 3, then 2 and then one.
We can multiply this:
5 * 4 * 4 * 3 * 3 * 2 * 2 * 1 * 1 = 2880
There are 2880 possibilities to form a line alternating them..
