# Combinatorics question

1. Sep 18, 2010

### Hypercubes

Probably the only area of math that really confuses me. I'm trying to calculate some probabilities for Liar's Dice. Essentially, the probabilities that a certain number of faces will appear when five dice are rolled, with one being a wildcard. If I try a specific combinatoric approach, for 5's for example, I get this. The numbers on each space represent the possible values:

Permutations that produce 0 5's: (2, 3, 4, 6)^5=4^5=1024
Permutations that produce 1 5: (1, 5)([2, 3, 4, 6]^4)=512
etc.

Already a problem emerges, as the chance of getting one 5 is higher than that of getting no 5's. If continued, it keeps dividing by two.However, if I use a general approach and ignore the wildcard property of ones, I get a (seemingly) correct answer, as when graphed it produces the familiar bell curve:
Permutations that produce 0 of anything: 5!=120 (don't quite understand the logic of this one)
Permutations that produce 1 of anything: (*)([2, 3, 4, 6]^4)=256
After that I can't figure out what I did, but here are the results:
120
256
320
80
20
1

What is the correct approach to this problem, and how to convert to probabilities?