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:(adsbygoogle = window.adsbygoogle || []).push({});

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?

Thanks in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Combinatorics question

**Physics Forums | Science Articles, Homework Help, Discussion**