June 16th, 2012, 05:07 AM  #31  
Math Team Joined: Apr 2012 Posts: 1,579 Thanks: 22  Re: Card fun Quote:
 
June 16th, 2012, 05:59 AM  #32 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: Card fun
For each of the five kinds of low card, you can either pick none (x^0 = 1), or one card in three ways (3x^1), two cards in three ways (3x^2), or three cards in one way (1x^3). The "y" is used as a tag to indicate that one kind of low card has appeared. For each of the six kinds of high card, you can either pick none (x^0) or one (1x^1). Now you are interested in hands of 5 cards, so you expand and look at the coefficient of x^5. The degree of y indicates how many different kinds of low card have been picked. There are 243 fivecard hands in which 5 kinds of low card appear, 4050 fivecard hands in which 4 kinds of low card appear, etc. 

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