Interesting Problems ? (permutations and combinations)

How do i do these questions?
1)How can the word DECISIONS be arranged so that the "N" is somewhere to the RIGHT of "D" (my problem is the two I's in particular)
ANSWER: 45360

2)Bob is about to hang 8 shirts in the wardrobe. He has 4 different styles of shirt, 2 identical ones of each particular style. How many different arrangements are possible if no 2 identical shirts are next to one another?
ANSWER: 864

3) A motorist travels through 8 sets of traffic lights, each of which is red or green. He is forced to stop at 3 sets of lights
a) In how many ways could this happen? ANSWER: 56
b) What other number of red lights would give an identical answer to part a)? ANSWER: 5

4) Find how many 5 digit numbers are possible from the digits 9,8,7,6,5,4,3,2,1,0 if digits are to be in
a) ascending order? ANSWER: 126
b) descending order? ANSWER: 252

Any help on any of these questions really appreciated !!

I suppose you know what factorials are, n!/k!(n-k)! is the amount of combinations you can make with k amount of elements in n without taking into account their order. An example is the I's S's in your first example, DECISIONS make up 9 letters so n=9. k=2 because there are two I's which you don't take into account order (try swapping the I's, you still have the same word). Calculating combinations 9C2 = 9!/2!(9-2!)= 9*8/2=36.
Next you do the same with the S's but since two letters are already in place so you have less places to put them in, namely 7 so now you have 7C2. If you go on you'll find that when k=1 then C is n.

For your second question, you can do it the same way, but remember that there is always one less place to put a shirt in because its next to the other.
I recommend you practice on the rest so you get the idea.