My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum

LinkBack Thread Tools Display Modes
January 19th, 2008, 09:40 AM   #1
Joined: Jan 2008

Posts: 3
Thanks: 0

Possibilities with a standard deck of cards?

First of all forgive me for the mistakes I'm gonna make. My english is in a very bad condition but wanted to try for an answer to my problem.
I have a standard deck of cards and I lay them all face up. There are 52! possible combinations that we can see.
But if the suit and colour dont matter, how many different combinations are? I mean that is we change place 2 cards with the same number (ex 8 of hearts and 8 of diamonds) we dont get a new combination.
Hope you understood my question
Thanks in advance
Krimi is offline  
January 19th, 2008, 12:07 PM   #2
Global Moderator
CRGreathouse's Avatar
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 938

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
(52!)/(4!)^13 = 92024242230271040357108320801872044844750000000000
CRGreathouse is offline  
January 19th, 2008, 12:38 PM   #3
Senior Member
Joined: May 2007

Posts: 402
Thanks: 0

There is a general formula. If you have a group of element's with n elements and k groups, each consisting of ki, 1>i>n, then you can rearrange the starting group in:

n!/(k1!*k2!*k3!*...*ki!) ways.

Therefore, if you have 52 cards and the color doesn't matter, you can rearrange it in:

52!/(4!)^13 ways just like CRGreathouse sad. This is because you have 13 groups each composed of 4 elements. Each group represents a card type (Jack, 10's..) and there are 4 of the cards in each group because there are four colors. You could solve the problem where the color does matter as:


Stupid, but true.
milin is offline  
January 19th, 2008, 07:52 PM   #4
Joined: Jan 2008

Posts: 3
Thanks: 0

I thank you both for your answer.
Milin I understood the way solving this through your post. Thanx for your explanation.
Krimi is offline  

  My Math Forum > High School Math Forum > Algebra

cards, deck, possibilities, standard

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
A deck of cards pedro malafaya Elementary Math 3 May 27th, 2013 07:56 AM
Probability with Deck of Cards flyingL123 Advanced Statistics 1 October 16th, 2011 10:05 PM
Deck of Cards Probability carolinegustin Probability and Statistics 3 March 27th, 2011 07:28 PM
Fair deck of 52 Cards wowbringer Algebra 1 March 17th, 2011 09:05 PM
Lightly or heavily shuffling a deck of cards Markgm Art 5 December 28th, 2010 07:59 AM

Copyright © 2019 My Math Forum. All rights reserved.