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?


Thanks in advance.
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 $P(K=k)=\frac{1}{5} \forall k$.
I believe that is the correct answer,

 - **Probability getting different email:**

       Based on your question given,
       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