Dice question

1. Feb 13, 2012

csc2iffy

1. The problem statement, all variables and given/known data

If someone could just check my work, thanks!
If five dice are rolled once each, what is the probability of rolling exactly 4 identical numbers?

2. Relevant equations

3. The attempt at a solution

This is what I have:
(1)(1/6)(1/6)(1/6)(5/6)=5/1296

2. Feb 13, 2012

Dick

That's the probability of doing it in a specific way. Say, first four identical, last one not identical. The problem doesn't specify any particular way.

3. Feb 13, 2012

csc2iffy

Ok, so would it be this instead?
(6)(1/6)3(5/6)

4. Feb 13, 2012

Dick

No. Why '6'? How many ways are there to choose the four identical dice out of five dice?

5. Feb 13, 2012

csc2iffy

i'm not sure, this is one of my study guide questions and this is why i'm asking...

6. Feb 13, 2012

Dick

Last edited: Feb 13, 2012
7. Feb 14, 2012

csc2iffy

I took a break from this problem but here is my newest attempt:
choose(5,4) = 5
so is it... 5(1/6)3(5/6)?

8. Feb 14, 2012

Dick

Well, yes. Doesn't that seem more right to you than the first try?

9. Feb 14, 2012

Ray Vickson

I think your basic approach is risky: you need to develop the answer step-by-careful step, rather than flailing around and writing down some almost random answers. If you need to keep asking "Am I right"?..."OK, what about now?..." it indicates that you are not at all confident about what you are doing. You would likely be more confident if you were more systematic. Ask yourself the following: suppose the 4 identical numbers are all 1. What would be the probability of that (that is, of getting 4 1's and 2 non-1's)? Think about getting four 2's (instead of 4 1's), then four 3's, etc. Does it matter what the number is? Can you put this all together?

RGV