Probability of cards

Question

How many numbers of possible live card hands (hands in five-card poker) drawn without replacement from a standard deck of 52 playing cards?

Please give full details!

Answer 1

combinations of 52 taken 5 at a time = 52C5 = 52!/47!5! = 2,598,960 hands

unless order of the cards dealt counts

then

permutations of 52 taken 5 at a time = 52P5 = 311,875,200 hands

Answer 2

This is the combination of 52 items taken 5 at a time. ₅₂C₅= 52(51)(50)(49)(48)/(5)(4)(3)(2)(1).

The following Desmos graph has a row that shows the "formula" that is used to calculate combinations. There is also a Desmos function for calculating combinations which is also shown.

desmos.com/calculator/srooowtjgd

Calculating this number is going to lead to questions like this:

1. What is the probability of getting dealt a flush?
2. Getting dealt a full house?

The number calculated above is going to be the denominator of the sample questions above.