Combinatorics Review - A little review on combinatorics: In...

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A little review on combinatorics: In general, you can ALWAYS USE THE BCR. However, combinations and permutations apply to very specific situations. However, when applicable, it is probably better to use a combination or permutation. Example: How many ways is it possible to get 2 pairs (and at best 2 pairs)? Using Combinations: There are “13 choose 2” ways to pick the 2 face values of the cards that you want pairs of. There are “4 choose 2” ways to get the suits of your pair. In addition, there are “11 choo se 1 ways” to pick the face value of the last card of your hand that is not the same as one of the first 2 cards. Also, there are “4 choose 1” ways that you can pick the suit for this final card. Therefore, the number of ways to get 2 pairs and only 2 pairs is: 1 4 * 1 11 * 2 4 * 2 13 2 . Now, think about attempting this with the BCR. More than likely, you would end up with the following: 13*4*3*12*4*3*11*4. This is double counting the number of ways suits can occur (4*3 since it is “ordering” the suits). A lso, there is a double count in the 2 cards you get for pairs (13*1 2 instead of “13 choose 2”). CLARIFICATION: The reason we are using “13 choose 2” instead of 13*12 is that we are not including the order in which they occur in your hand. Also, there is no essential difference between the first face value
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This note was uploaded on 02/06/2012 for the course STAT 225 taught by Professor Martin during the Spring '08 term at Purdue University-West Lafayette.

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Combinatorics Review - A little review on combinatorics: In...

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