Question

What is the probability of getting a hand of two clubs and three diamonds?

Answer 1

`(13/52xx12/51xx13/50xx12/49xx11/48)xx""^5C_2 = 267696/31187520`

`~~ .008583433373349339`

That is about `1` in `116`

Explanation:

The probability of being dealt two clubs then three diamonds is:

`13/52xx12/51xx13/50xx12/49xx11/48`

But we don't mind what order we get these cards, so this probability needs to be multiplied by `""^5C_2 = (5!)/(2!3!) = (5xx4)/2 = 10` to represent the number of possible orders of clubs and diamonds.