# Multinomial distribution

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• December 8th 2010, 06:27 PM
holly123
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)

Thanks in advance!!
• December 8th 2010, 07:05 PM
pickslides
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?
• December 9th 2010, 06:27 AM
holly123
No I cannot think of any other ways. And I don't know how to solve for the probability still
• December 9th 2010, 06:32 AM
Plato
The number of ways:
• zero times $4^5$
• one time $(5)(4)(4^3)$
• two times $\binom{5}{2}\binom{3}{2}(4)$

Now divide by $6^5$
• December 9th 2010, 09:58 AM
holly123
That makes sense but does not give me the answer in the back of the book of 2424/(6^5)
• December 9th 2010, 10:12 AM
holly123
Never mind, I figured it out. That 3 should be a 2 above
• December 9th 2010, 10:42 AM
Plato
Quote:

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