INTRODUCTION TO PROBABILITY In Texas Hold’em poker a player receives 2 cards fir

Question

INTRODUCTION TO PROBABILITY

In Texas Hold’em poker a player receives 2 cards first. These are called the player’s pocket cards. Find the number of pocket card configurations (that is, the number of unordered samples of two cards from the deck of 52) that correspond to the following descriptions.

(a)   Pair. (The two cards have the same rank.)

(b)   Suited. (The two cards have the same suit.)

(c)   Suited connectors. (The two cards have the same suit, and their ranks are next to each other. An ace has a special role: both {A, 2} and {K, A} count as pairs of neighbors.)

Explanation / Answer

Total number of all possible unordered samples of 2 cards from deck of 52 cards = 52C2

1. Total number of possible Pairs (cards of same ranks) = 13C1 (No of ways of choosing a particular rank) * 4C2 (No of ways of choosing 2 out of 4 suits given a rank)

= 78

2. Total number of possible suited cards = 4C1 (No of ways of choosing 1 out of 4 suits) * 13C2 (No of ways of choosing 2 cards from 13 of a given suit) = 312

3. Total number of possible suited connectors = 4C1 (No of ways of choosing 1 out of 4 suits) * 13 (Total number of neighbour pairs given a suit : {A,2}, {2,3} .... {Q,K} , {K,A} )

= 52

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