Answer:
There are 2,598,960 5 draw poker hands are there.
There are 311,875,200 5-stud poker hands.
Step-by-step explanation:
When the order is not important, we use the combinations formula:
For example, eating an apple and an orange is the same as eating an orange and an apple.
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
When the order is important, we use the permutations formula:
For example, a 3 digit credit card password, 123 is different than 213.
The number of possible permutations of x elements from a set of n elements is given by the following formula:
![P_{(n,x)} = \frac{n!}{(n-x)!)}](https://tex.z-dn.net/?f=P_%7B%28n%2Cx%29%7D%20%3D%20%5Cfrac%7Bn%21%7D%7B%28n-x%29%21%29%7D)
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?
Here, the ordering is not important, so we use the combinations formula.
![C_{52,5} = \frac{52!}{5!47!} = 2598960](https://tex.z-dn.net/?f=C_%7B52%2C5%7D%20%3D%20%5Cfrac%7B52%21%7D%7B5%2147%21%7D%20%3D%202598960)
There are 2,598,960 5 draw poker hands are there.
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?
The ordering is important, so we use the combinations formula.
![P_{(52,5} = \frac{52!}{47!)} = 311875200](https://tex.z-dn.net/?f=P_%7B%2852%2C5%7D%20%3D%20%5Cfrac%7B52%21%7D%7B47%21%29%7D%20%3D%20311875200)
There are 311,875,200 5-stud poker hands.