Help with combinations, permutations and counting please?

A group of 30 people consists of 15 women and 15 men.

How many ways are there to:

1) Pair the women and men off?( I got 15! as the first guy has 15 women to choose from , the second has 14 etc. is this correct?)

2) Form 10 pairs from the group? (This is non-gender specific so you first choose 20 People from the group =C(30,20)? but what do you multiply it with to get the pairs? Or am I completely wrong about the first half?)

3) Divide the group into two groups (group 1 and 2) of equal size? (Is this just choosing 15 people from 30 = C(30,15)?)

4) Divide the group into two equal groups, where each group in its own has as many women as men in it? (would this be taking 7 men from 15 and multiplying it by taking 7 women from 15? I'm now officially lost and hopelessly confused?)

5) Divide the group into two groups of equal size, such that group 1 contains at least 4 men? (I don't have a clue. Choose 15 from 30 people multiplied by C(15,4)?)

6) Divide the group into two groups each having size at least 1?(C(30,1)?)

Help with formulae and explanations would help majorly. Thanks in advance