In how many different combinations can a deck of cards be shuffled?

Question

In how many different combinations can a deck of cards be shuffled?

Question #149590. Asked by serpa.
Last updated Aug 08 2023.
Originally posted Aug 05 2023 5:11 PM.

psnz

Answer has 2 votes

psnz

5 year member
1007 replies avatar

Answer has 2 votes.

52! or factorial 52. This number is approximately 8x10^67. The title of the following article is particularly relevant when considering the magnitude of that number:

There are more ways to arrange a deck of cards than there are atoms on Earth

https://www.mcgill.ca/oss/article/did-you-know-infographics/there-are-more-ways-arrange-deck-cards-there-are-atoms-earth

Aug 05 2023, 5:37 PM

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Answer 1

Just to explain the factorial process. 52! means that all the numbers from 1 up to and including 52 are multiplied together: 1 x 2 x 3 x 4 x 5 x 6 x ... x 50 x 51 x 52. Factorial numbers get really big really quickly!
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040

Answer 2

wellenbrecher

Answer has 0 votes

wellenbrecher

20 year member
650 replies

Answer has 0 votes.

Here's an interesting explanation how to shuffle a deck in order to completely randomize it:

https://www.youtube.com/watch?v=AxJubaijQbI

Aug 08 2023, 3:15 PM

In how many different combinations can a deck of cards be shuffled?

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