Rolling 4 Identical Numbers: Probability

[csc2iffy]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

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

 

[Dick]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

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

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.

 

[csc2iffy]

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

 

[Dick]

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

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

 

[csc2iffy]

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

 

[Dick]

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

How many ways to choose 4 objects from 5? It's a binomial coefficient. It's a combinatorial thing. http://en.wikipedia.org/wiki/Binomial_coefficient

 

[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)?

 

[Dick]

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)?

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

 

[Ray Vickson]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

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

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