The Probability of Getting Dealt 4-of-a-kind

Date: 21 Mar 1995 20:35:54 -0500
From: Anonymous
Subject: HELP

Would you help me solve this problem:

What is the probability of being dealt 5 cards and 
getting four of a kind? (e.g. four aces and the 3 of 
hearts).  Thanks much for your help and time.

                     PH(online)

Date: 23 Mar 1995 10:43:17 -0500
From: Dr. Ken
Subject: Re: HELP

Hello there!

Well, keep in mind the general formula when trying to 
find probabilities:

                          # of favorable cases
                          --------------------
                            total # of cases

If you can figure out the total number of different hands 
(of any kind) you can be dealt, that will be the denominator.  
The numerator will be the number of different ways you 
can get four of a kind.  Think about this:  you can have the 
four cards that are the same be any one of thirteen cards, 
and the other card be any one of twelve (once you've 
already chosen which cards are in the four of a kind).  So 
how many different ways can you get four of a kind?

Hope this helps.  Write back if you're still confused.

-Ken "Dr." Math