View Full Version : Finding amount of different 5 card hands

05-05-2005, 12:18 AM
This was a question tonight in a team trivia game, the maximum amount of different 5 card hands.

I was fairly frustrated that I did not come up with the answer, as my method of solving was 52*51*50*49*48. This turned out to be very wrong.

The answer ended up being something around 2.6 million. How is this mathematically solved? Basic stuff, probably.

Thanks in advance.

05-05-2005, 02:36 AM
You were on the right track.

It's the same 5-card hand no matter which order you are dealt the five cards.

So, 52*51*50*49*48 / (5*4*3*2*1), which is, indeed, just under 2.6 million.

05-05-2005, 09:44 AM
Its call the Binomial Coefficients:

n choose x = n! / ((n - x)! * x!)

Where n = 52 cards and x = 5 card hands

Here is a link to Binomial Coefficients (http://mathworld.wolfram.com/BinomialCoefficient.html)

Hope that gives you the overview.