Consider the set of all possible five-card poker hands dealt fairly from a standard deck of

fifty-two cards. How many atomic events are there in the joint probability distribution?

Concept:

A joint probability distribution shows a probability distribution for two or more random variables. It looks for a relationship between two variables say x and y. It gives the probability that each x and y falls in a particular range of set of values specified for that variable.

Explanation:

Here, given:

Total cards = 52

We have to deal with 5 cards.

In this question, atomic events possible can be find in the number of ways they can be combined.

Which is represented as C (n, r) = (n!)/ (n-r)! r!

Here n = 52

r = 5

C (52, 5) = (52)! / (5)! (52 - 5)!

C(52, 5) = \(\frac{{52 \times 51 \times 50 \times 49 \times 48 \times 47!}}{{5 \times 4 \times 3 \times 2 \times 1 \times 47!}}\) 

C(52, 5) = 2, 598, 960