Chapter 9.1, Problem 28E

Solution

To state: The number of “straight” poker hands that can be formed if a five card hand is dealt from a standard deck of 52.

The resultant“straight” poker card hands are $2,598,960$ .

Given information:

A five card hand is dealt from a standard deck of 52.

Explanation:

Consider the given information,

There are 52 cards in a deck. For forming possible “straight” poker hands 5 cards are to be used. As by assuming there is no order for the 5 card.

There is combination counting formula use. Then total number of ways that can combine n objects taken r at a time is given by:

  $C{}_r=\frac{n!}{r!\left(n-r\right)!}$

Total number of card: 52

Number of cards in a hand: 5

  $\begin{array}{c}{C}_{{52}_5}=\frac{52!}{5!\left(52-5\right)}\\ =\frac{52!}{5!47!}\\ =\frac{52\cdot 51\cdot 50\cdot 49\cdot 48\cdot 47!}{5!47!}\\ =\frac{52\cdot 51\cdot 50\cdot 49\cdot 48}{5\cdot 4\cdot 3\cdot 2\cdot 1}\\ =\frac{311875200}{120}\\ =2,598,960\end{array}$

Therefore, the number of possible straight poker hands is $2,598,960$ .