1. ## Multinomial distribution

If five balanced dice are rolled, what is the probability that the number 1 and the number 4 will appear the same number of times?

I know that n=5, but I can't figure out what other numbers to plug into the equation. 1 can appear once and 4 can appear once, or 1 can appear twice and 4 can appear twice. Anyone know how to do this??? The answer in the book is (2424)/(6^5)

2. So this includes the occurance that of the 5 dice.

both #1 and #4 appear once together
both #1 and #4 appear twice together
both #1 and #4 appear not at all

Can you think of any other ways?

3. No I cannot think of any other ways. And I don't know how to solve for the probability still

4. The number of ways:
• zero times $\displaystyle 4^5$
• one time $\displaystyle (5)(4)(4^3)$
• two times $\displaystyle \binom{5}{2}\binom{3}{2}(4)$

Now divide by $\displaystyle 6^5$

5. That makes sense but does not give me the answer in the back of the book of 2424/(6^5)

6. Never mind, I figured it out. That 3 should be a 2 above

7. Originally Posted by holly123
That makes sense but does not give me the answer in the back of the book of 2424/(6^5)
I get the same as your text book: 2424