Probability: Permutations/Combinations

[catbearbig]

I'm having a hard time understanding how to derive the # ways to do things.

(a) A course has 4 sections with no limit on how many can enrol in each section. 3 students each pick a section at random.

(i) Specify Sample Space S (64?)
(ii)Find the probability that they all end up in the same section (3C1 /64 = 3/64??)
(iii) Find the probability that they all end up in different sections (3P3/64 = 6/64 ??)
(iv) Find the probability that nobody picks section 1 ( 3C2 * 2! / 64 = 6/64??)

(b) Repeat (a) in the case where there are n sections and s students.

Can someone please help me derive their answers of how they get the # of ways to do each. Thanks a lot!

[Joffan]

I suggest, first, that you check the top thread on how to present a homework problem. Or look at the standard layout used by most others.

For your probability answer, don't forget there are 4 sections, not 3. And a little more explanation of your thinking would help others to help you.