Combinatorics Review

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 4

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online