Question

What is the theoretical probability of being dealt exactly two 10's in a 5-card hand from astandard 52-card deck?

Answer 1

The theoretical probability is 0.04 (2162/54145)

Here, we want to find a theoretical probability

A five card hand means a selection of five cards from a total of 52

Before we go on to answer, we need to know the number of 10's in a standard deck of cards

In a deck of cards, there are 4 suites, with each suites having a single 10

So in total, there are 4 10's

Out of the 52 cards, we are selecting five cards

The number of ways we can do this can be calculated using combination

This will be;

`52\text{ C 5 = }2,598,960`

Out of the 4 available 10's, we are selecting 2

The number of ways we can do this is;

`4\text{ C 2 = 6 ways}`

Now, out of the remaining 48, we are selecting 3

The number of ways to do this will be

`48\text{ C 3 = 17,296}`

So the theoretical probability would be;

`\frac{17,296\text{ }*\text{ 6}}{2,598,960}\text{ = 0.0399 which is 0.04}`

This is same as; 2162/54145