My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 15th, 2012, 08:15 AM   #1
Newbie
 
Joined: Sep 2012

Posts: 2
Thanks: 0

Card Combinations

I have a problem that needs solving:

From a pack of 52 cards, how do you select three cards that have these specific properties.

1. Two of these cards must be of the same rank.
2. The third of these cards must be of a rank that is two gaps higher or lower than the other two cards.
3. All three cards must be of a different suit.
4. The result must be expressed as a combination (not a permutation).

So the combination 6spades 6clubs 9hearts fits in this category. As does 6hearts 6diamonds 3clubs also fit in this category.

Instead of just producing an answer I would really appreciate if someone could explain the reasoning behind the result.
nuerofuzz is offline  
 
September 15th, 2012, 09:42 AM   #2
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,413
Thanks: 1024

Re: Card Combinations

Quote:
Originally Posted by nuerofuzz
2. The third of these cards must be of a rank that is two gaps higher or lower than the other two cards.

So the combination 6spades 6clubs 9hearts fits in this category. As does 6hearts 6diamonds 3clubs also fit in this category.
Why do your examples show 3 gaps?

KingHearts KingSpades ... is there a HIGHER gap card?

AceHearts AceSpades ... is there a LOWER gap card?
Denis is offline  
September 15th, 2012, 12:24 PM   #3
Newbie
 
Joined: Sep 2012

Posts: 2
Thanks: 0

Re: Card Combinations

Just to claritify, 663 represents a two card gap. The gap would comprised of 5 and 4. As would be the case with 669, the gap being 7 and 8. And because the 13 card rankings can be counted cyclically then one could have AA4 or AAJ. Both combinations would represent a pair and a two card gap.
nuerofuzz is offline  
September 15th, 2012, 12:49 PM   #4
Math Team
 
Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: Card Combinations

Hello, nuerofuzz!

Quote:
From a pack of 52 cards, how do you select three cards that have these specific properties.

1. Two of these cards must be of the same rank.
2. The third of these cards must be of a rank that is two gaps higher or lower than the other two cards.
3. All three cards must be of a different suit.
4. The result must be expressed as a combination (not a permutation).

So the combination fits in this category.
As does also fit in this category.

And the ranks are cyclic.









soroban is offline  
September 15th, 2012, 08:50 PM   #5
Math Team
 
Joined: Oct 2011
From: Ottawa Ontario, Canada

Posts: 14,413
Thanks: 1024

Re: Card Combinations

6C 6D ; 3H or 3S or 9H or 9S = 4 ways ; similarly for 5 more:
6C 6H
6C 6S
6D 6H
6D 6S
6H 6S
So that's 6 * 4 = 24

With 13 ranks: 13 * 24 = 312

How do you get 624, Soroban?
Denis is offline  
September 15th, 2012, 10:06 PM   #6
Math Team
 
Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: Card Combinations

Hello, Denis!

You're absolutely right!


Quote:
Originally Posted by I



I imparted an order to the first two cards . . . *blush*

soroban is offline  
Reply

  My Math Forum > College Math Forum > Advanced Statistics

Tags
card, combinations



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Card fun Denis Algebra 31 June 16th, 2012 05:59 AM
A Card Probability Erimess Probability and Statistics 4 May 10th, 2011 09:14 PM
Complex Combinations Within Combinations Problem? bugrocket Advanced Statistics 2 January 23rd, 2011 04:02 PM
"Pick a card, any card" probability question Niko Bellic Probability and Statistics 1 March 18th, 2010 01:15 PM
Card box bernando Applied Math 2 July 3rd, 2007 06:21 PM





Copyright © 2019 My Math Forum. All rights reserved.