# Probability: Permutations/Combinations

1. Jan 17, 2012

### 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.