Probability Permutations and Combinations

Hello there,

I have quite a few questions that I need some help for. I don't specifically require the answers, just the means/methods for figuring them out, then I can reply with my attempts. There's a few:

1) A committee is selected from 7 men and 6 women.

i) How many ways are there for a committee consisting of 3 men and 3 women?

ii) How many ways for a committee of size 6 with one particular man and one particular women?

2) i) In how many ways can the letters "abceeee" be arranged so that no "e" is adjacent to another "e"?

ii) There are 20 seats on a bus. In how many ways can 3 people be seated in the bus?

3) a) A box contains 10 memory sticks of which 4 are defective. Three memory sticks are drawn randomly without replacement. Find the probability that:

i) they are all defective

ii) only one is defective.

iii) none of them are defective.

(apparently supposed to be shown in real numbers to 3s.f and simplified rational numbers).

4) A fair coin is tossed three times. Cnsider the events:

A. TAILS on second toss

B TAILS on third toss

C TAILS on exactly one coin

i) Find P(A), P(B) and P(C)

ii) Find P(A n C) and decide whether it represents an independant event or not.

Again, the methods or some guidance is good. I'd like to learn this myself. Thanks will be given!

Regards,