Sign in or 
Share this
5.2 Combinations...
5.2 Combinations
A combination is a selection of objects in which order is not important. The number of combinations of objects chosen from a set of objects is: 
In general, the sum of all the combinations of n distinct things is 2n.
Example: You have 5 shirts, but you can only select 3 for your vacation. In how many different ways can you do this?
=10, the order in which you select the shirts, does not matter.
Example: You are going to draw 7 cards from a standard deck of 52 cards. How many different 7 card hands are possible? This is a combination problem, because a hand is a group of cards where order does not matter. First we need to find n and r:
n= 52, there are 52 cards in a deck of cards.
r = 7, the number of cards that need to be drawn
nCr = n! / (n-r)!r!
52C7 = 52! / (52-7)!7!
= 52! / (45! 7!)
= (52 * 51 * 50 * 49 * 48 * 47 *46 * 45! ) / (45! * 7!)
= (52 * 51 * 50 * 49 * 48 * 47 * 46) / (7 * 6 * 5 * 4 * 3 * 2 * 1)
= 133784560
Example: There are 12 boys and 14 girls in Mrs. Smith’s math class. Find the number of ways Mrs. Smith can select a team of 3 students from the class to work on a group project.
The team consists of 1 girl and 2 boys.
Boys: Girls:
References
Canton, Barbara J., Erdman, Wayne, Irvine, Jeff, Lim, Louis, Mclaren, Fran, Meisel,Roland W., Miller, David T., Speijer, Jacob. (2002). Mathematics of Data
Management. Toronto: McGraw - Hill.
rajdua |
Latest page update: made by rajdua
, Oct 24 2007, 10:05 PM EDT
(about this update
About This Update
Edited by rajdua
70 words added 1 image deleted view changes - complete history) |
|
Keyword tags:
combinations
More Info: links to this page
|
| Started By | Thread Subject | Replies | Last Post | ||
|---|---|---|---|---|---|
| Anonymous | Using the knowledge | 0 | Nov 23 2007, 3:25 AM EST by Anonymous | ||
|
|
Thread started: Nov 23 2007, 3:25 AM EST
Watch
I think this page is great.... but if you want to apply the knowledge or get a better understanding you should visit 5.3 problem solving with combinations. Trust me that will help more.
|
||||
| Anonymous | something wrong with first example | 2 | Oct 23 2007, 9:10 AM EDT by Anonymous | ||
|
|
Thread started: Oct 22 2007, 10:05 PM EDT
Watch
hey! i think there is something wrong with first example (52-7) is 45 not 48 and final ans. of question is 133784560.
|
||||
| Pacek89 | Phil, Shadi, and Larry- Great Page | 0 | May 31 2007, 9:43 PM EDT by Pacek89 | ||
|
Thread started: May 31 2007, 9:43 PM EDT
Watch
The spacing, the headers and titles, everything seems right on. You've made this page work without the use of pictures, which our group thought was impossible for our own wiki. A lot of the explanations are original as well as accurate in the presentation and explanation. Great job.
|
|||||
Showing 3 of 8 threads for this page
- view all
