There are 270725 different ways to select 4 from 52 cards if I don't care about the order of cards in my hand.
Permutation and combination: The process of ordering objects or numbers is known as permutation. Combinations are a method of choosing items or numbers from a collection or group of items so that the order of the items is irrelevant.
Combinations are used to group objects or to determine how many subgroups can be formed from the given collection of objects. Additionally, we use permutations to determine the number of potential combinations of unrelated objects.
For example, if we want to select 2 players from 6. This will be:
= 6! / 2! (6 - 2)!
= 15 ways
In the given question use the combination. We can write as:
[tex]52C_{4}[/tex] = 52!/4! (52-4)!
This expression could be written in the form
[tex]52C_{4}[/tex] = 52!/4! (52-4)!
[tex]52C_{4}[/tex] = 52!/(4! (48)!)
[tex]52C_{4}[/tex] = 52 x 51 x 50 x 49 x 48!/(4 x 3 x 2 x 48!)
As, 48! cancel out. We get,
[tex]52C_{4}[/tex] = 52 x 51 x 50 x 49/24
= 6497400/24 = 270725
Hence, there are 270725 ways.
To learn more about combination visit: https://brainly.com/question/29594894
#SPJ4
