A hand of 5-card draw poker is a simple random sample from the standard deck of 52 cards. How many 5 draw poker hands are there?

Question

2 months ago

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In 5-card stud poker, the cards are dealt sequentially and the order of appearance is important. How many 5-stud poker hands are there?

1 answer:

babunello [11.8K] · Answer 1 · 2026-03-25T07:52:01+03:00

Answer:

The total number of possible 5-card draw poker hands amounts to 2,598,960.

For 5-stud poker hands, that number is 311,875,200.

Step-by-step explanation:

When the order of the items is not a factor, the combinations formula is utilized:

For instance, consuming an apple and an orange is regardfully the same as having an orange and then an apple.

$C_{n,x}$ denotes the combinations of x items chosen from a pool of n elements, calculated via this equation.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

However, if the order matters, we implement the permutations formula:

For example, the 3 digit code 123 is distinct from 213.

The permutations of x elements from n total elements can be found with this formula:

$P_{(n,x)} = \frac{n!}{(n-x)!)}$

A 5-card draw poker hand randomly samples from the standard 52-card deck. How many such hands can be formed?

In this case, order is irrelevant, so we apply the combinations formula.

$C_{52,5} = \frac{52!}{5!47!} = 2598960$

The total number of 5-card draw poker hands is 2,598,960.

In 5-card stud poker, cards are dealt one after another, making the order essential. Thus, how many 5-stud poker hands can we create?

As the order matters, we utilize the combinations formula.

$P_{(52,5} = \frac{52!}{47!)} = 311875200$

The total number of 5-stud poker hands equals 311,875,200.