S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
It is currently Mon, 20 May 2013 07:52:15 UTC

All times are UTC [ DST ]




Post new topic Reply to topic  [ 3 posts ] 
Author Message
 Post subject: count of combinations of differences in a 6/49 lottery
PostPosted: Thu, 28 Jun 2012 10:25:10 UTC 
Offline
Senior Member

Joined: Mon, 29 Aug 2011 17:11:42 UTC
Posts: 62
Say we have a 6/49 lottery.
The ticket has 6 numbers out of 49.
Say the ticket is always sorted from left to right, from smallest number in it to largest.
The differences between those numbers are 5.

What is the total possible count of combinations of these differences?
Order is not important obviously, and also there are no repetitions of numbers in them.

49 48 47 46 45 44 => biggest difference that can be is 44, or, 49 48 47 46 45 - 1 = 44

C(44,5)=1086008 possibilities
preliminary probability of one being extracted (not for any of them actually):
C(5,5)C(39, 0)/C(44,5) = 1/1086008?


Top
 Profile  
 
 Post subject: Re: count of combinations of differences in a 6/49 lottery
PostPosted: Thu, 28 Jun 2012 13:13:59 UTC 
Offline
Senior Member

Joined: Mon, 29 Aug 2011 17:11:42 UTC
Posts: 62
I meant to say there are no repetitions in the lottery numbers, the differences between those numbers can have the same cardinality or value


Top
 Profile  
 
 Post subject: Re: count of combinations of differences in a 6/49 lottery
PostPosted: Sat, 30 Jun 2012 10:48:59 UTC 
Offline
Member of the 'S.O.S. Math' Hall of Fame
User avatar

Joined: Mon, 23 Feb 2009 23:20:33 UTC
Posts: 1049
Location: Adelaide, Australia
Let P(n,k) be the number of partitions of n into k parts.
Then the number of sequences of differences, treating permutations of a sequence as identical, is

.....$\sum_{n=5}^{48}P(n,5)\,=\,23531

Note that these sequences have greatly varying probabilities.


Top
 Profile  
 
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 3 posts ] 

All times are UTC [ DST ]


Who is online

Users browsing this forum: No registered users


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum

Search for:
Jump to:  
Contact Us | S.O.S. Mathematics Homepage
Privacy Statement | Search the "old" CyberBoard

users online during the last hour
Powered by phpBB © 2001, 2005-2011 phpBB Group.
Copyright © 1999-2013 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA