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;
[tex]52\text{ C 5 = }2,598,960[/tex]Out of the 4 available 10's, we are selecting 2
The number of ways we can do this is;
[tex]4\text{ C 2 = 6 ways}[/tex]Now, out of the remaining 48, we are selecting 3
The number of ways to do this will be
[tex]48\text{ C 3 = 17,296}[/tex]So the theoretical probability would be;
[tex]\frac{17,296\text{ }\times\text{ 6}}{2,598,960}\text{ = 0.0399 which is 0.04}[/tex]This is same as; 2162/54145
