Combonatorics + Probability

I'm trying to study for an exam, any/all help would be fantastic. I'm having trouble with these specific questions:

1) In how many ways can 9 examination questions be arranged so that the easiest and most difficult do not immediately follow each other?

The answer is 7*8!, But I'm not sure why.---

2) Four cards are drawn from a deck of 52 playing cards without any replacement. Find the probability that all the cards are hearts.

What is the probability of tossing a coin five times and having heads come up each time? ---

3) Six balls are selected from a bag, at random and without replacement. Before the selection the bag contained eight red balls and nine yellow balls.

b) How many red balls should you expect to pull out of a bag?---

4) Going into a football game, a field goal kicker had been successful on 80% of field goal attempts. During the game he had five field goal attempts.

a) based on his previous performance, what is the probability of his being successful on all five kicks in this game?

c) what is the probability that his first successful attempt will be on the last kick of the game?---

We think the answer to #2 is:

13/52 * 12*51 * 11*50 * 10/49

4a must be .8 * .8 * .8 * .8 * .8

4c must be .2 * .2 * .2 * .2 * .8

The unnumbered problem: The probablity of 5 heads

.5 * .5 * .5 * .5 * .5

For 3b the most likely number must be 3 or 1/2 of 6 because there are two approximately equal set of balls.

For question one, we think that the number of possible permutations is 9! and the unpermitted permutations is 14*7!. The permitted permutations should be:

9! - 14*7!

72*7! - 14*7!

58*7!