Question

What is the probability of a player having single pair card combination in a game of poker

Answer 1

Answer:

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Answer 2

Given:

The game of poker is played

To Find:

The probability of a player having a single pair card combination

Explanation:

The Formula of the Combination is

$_{}^{n}\textrm{C}_{r} =\dfrac{n!}{(r!\times(n-r)!)}$

The Total number of ways for the selection of $5$ cards

$_{}^{52}\textrm{C}_{5}$$=\d2598960$

Number of ways to have single pair

$=(_{}^{13}\textrm{C}_{1})\times(_{}^{4}\textrm{C}_{2})\times(_{}^{12}\textrm{C}\x_{3})\times(_{}^{4}\textrm{C}_{1})^{3}$

$=1098240.$

Probability to have single pair

$=\dfrac{Number\ of\ ways\ to\ have\ single\ pair}{Total\ ways\ of\ selection\ of\ 5\ cards} \\=\dfrac{1098240}{2598960}$

$=0.4226$

The probability of a player having a single pair combination is $0.4226$.