# Probability of emails

can anyone can enlighten me on how to solve this? Are there any good approaches to tackle this kind of problem?

The sizes of e-mail messages received could be 1K bytes, 2K bytes, 3K bytes, 4K bytes or 5K bytes. All sizes are equally likely. What is the probability that 6 incoming emails comprise one 3K byte message, three 4K byte messages and two 5K byte messages?

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Hint: Step 1, what is the probability that the first message is 3K, the next three are each 4K, and the last two are 5K. Step 2, consider different orders for these desired outcomes. – vadim123 May 5 '13 at 4:30
@vadim123: This is a good hint that should be posted as an answer. – Ross Millikan May 5 '13 at 4:31
@Ross, thanks; most of the time when I post a hint as an answer, someone simultaneously posts a complete answer and gets all the attention anyway. – vadim123 May 5 '13 at 4:33
@vadim123: True, that happens a lot. I would prefer your hint, but others prefer to show off. I would like to be able to upvote your answer (which I have done to the comment, but it doesn't get you any rep). – Ross Millikan May 5 '13 at 4:39

You can use the Multinomial Distribution.

For $n$ independent trials each of which leads to a success for exactly one of $k$ categories, with each category having a given fixed success probability, the multinomial distribution gives the probability of any particular combination of numbers of successes for the various categories.

In your case: $n=6$, $k=5$, and $P(K=k)=\frac{1}{5} \forall k$.

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I believe that is the correct answer,

 - **Probability getting different email:**

P(1k)=P(2K)=P(3K)=P(4K)=P(5K)=1/5
(But it is not important issue)

I believe the problem is related to the combination (nCr) to be used

Total 6 emails
= one 3Kbyte email + three 4Kbytes email + two 5Kbytes email
= 6C1 x 6C3 x 6C2 *(or =COMBIN(6,1) * COMBIN(6,3) * COMBIN(6,2) from excel)*
= 6 x 15 x 20
= 1800

Total combination of 6 emails for 5 kinds of emails
= 5 ^ 6
= 5 * 5* 5* 5* 5 * 5
= 15625


So the actual probability is =1800 / 15625 =0.1152

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This doesn't ask OPs question, I'm afraid: he asked for help on how to solve it, not for an answer without any explanation at all. – HSN May 6 '13 at 9:09