# Homework Help: What is the probability of getting 1,2,3,4 when 5 dice are thrown and

1. Nov 4, 2012

### MilenaMath

What is the probability of getting 1,2,3,4 when 5 dice are thrown and one of them is not 5.(the order of 1,2,3,4 doesnt matter)
I am really confused:
So I computed chances of getting correct numbers that is 1/6^4 times 5/6,then I multiply this by 4 times 5! Am I right?

2. Nov 4, 2012

### haruspex

Re: Probability

Your question is unclear. Do you mean at least one each of 1, 2, 3, 4? Exactly one of each?
When you say one of them is not five, do you mean that a particular one is not five, that they are not all five, or that none of them are five?

3. Nov 4, 2012

### MilenaMath

Re: Probability

I need to get exactly 1,2,3,4(order doesnt matter) and the fifth dice can be whatever number but 5

4. Nov 5, 2012

### haruspex

Re: Probability

Sorry, still not clear. If you get 4, 2, 2, 3, 1, is that ok or not?

5. Nov 5, 2012

### Ray Vickson

Re: Probability

From this description, it seems the event you want is
A = {1,1,2,3,4} or {1,2,2,3,4} or {1,2,3,3,4} or {1,2,3,4,4} or {1,2,3,4,6}, but without regard for order. Is that correct? If so, you can use a multinomial distribution to find
P{A} = p(2,1,1,1,0,0) + p(1,2,1,1,0,0) + ... + p(1,1,1,1,0,1), where these are the occupancy numbers in each of the 6 classes 1--6.

RGV