Monday, November 18, 2019
10:41 AM (GMT +5)

Go Back   CSS Forums > CSS Optional subjects > Group II > Statistics

Reply Share Thread: Submit Thread to Facebook Facebook     Submit Thread to Twitter Twitter     Submit Thread to Google+ Google+    
 
LinkBack Thread Tools Search this Thread
  #1  
Old Wednesday, July 07, 2010
Junior Member
 
Join Date: Jun 2010
Location: hyderabad
Posts: 5
Thanks: 1
Thanked 4 Times in 3 Posts
soha rao is on a distinguished road
Default Rules of Permutation and Combination

Permutation
Permutation is an ordered arrangement of a number of elements of a set.

Mathematically, given a set with n numbers of elements, the number of permutations of size r is denoted by P(n,r) or nPr or nPr.
The formula is given by

P(n,r) = nPr = nPr = n!
(n - r)!

where n! (n factorial) = n (n-1) (n-2) ... 1 and 0! = 1.

For example, given the set of letters {a,b,c} the permutations of size 2 (take 2 elements of the set) are {a,b}, {b,a}, {a,c}, {c,a}, {b,c}, and {c,b}. Please note that the order is important (i.e. {a,b} is considered different from {b,a}).
The number of permutations is 6.

P(3,2) = 3P2 = 3P2 = 3!
(3 - 2)!
= 3 2 1
1!
= 6
1
= 6

Another example: How many different ways are there can 5 different books be arranged on the self?

Answer: Here, n = 5 and r = 5.
So, 5P5 = 5!/(5-5)! = 5!/0! = (5 4 3 2 1)/1 = 120.

As can be seen from the above example, when n = r, the formula for nPr = n!.


--------------------------------------------------------------------------------

Combination
Combination is an unordered arrangement of a number of elements of a set.

Given a set with n numbers of elements, the number of combinations of size r is denoted by C(n,r) or nCr or nCr.
The formula is given by

C(n,r) = nCr = nCr = n!
r! (n - r)!

where n! (n factorial) = n (n-1) (n-2) ... 1 and 0! = 1.

For example, given the set of letters {a,b,c} the combinations of size 2 (take 2 elements of the set) are {a,b}, {a,c}, and {b,c}. Please note that the order is not important (i.e. {b,b} is considered the same as {a,b}).
The number of combinations is 3.

C(3,2) = 3C2 = 3C2 = 3!
2! (3 - 2)!
= 3 2 1
2 1 1!
= 6
2
= 3

Another example: A basket contains an apple, an orange, a pear, and a banana. How many combinations of three fruits are there?

Answer: Here, n = 4 and r = 3.
So, 5C5 = 4!/3!(4-3)! = (4 3 2 1)/(3 2 1) 1! = 24/6 = 4.

For combination when n = r, the number of combinations is always equal to 1.
__________________
"""always bee happyy and work hard"""
Reply With Quote
The Following User Says Thank You to soha rao For This Useful Post:
safdarrao (Saturday, July 10, 2010)
  #2  
Old Saturday, July 10, 2010
Junior Member
 
Join Date: May 2010
Posts: 1
Thanks: 1
Thanked 0 Times in 0 Posts
safdarrao is on a distinguished road
Post

In the formulae aforementioned for Permutation & Combination , the sign of division '/' is either missing or I'm unable to see it, at least. In my humble opinion, correct formulae are as follows :
P(n,r) = nPr = n! / (n-r)!
and
C(n,r) = nCr = n! / r! (n-r)!
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
More Than 2000 Words to enhance Vocabulary Qurratulain English (Precis & Composition) 23 4 Weeks Ago 02:13 PM
Notes and Topics on Statistics Faraz_1984 Statistics 23 Saturday, June 04, 2011 08:08 AM


CSS Forum on Facebook Follow CSS Forum on Twitter

Disclaimer: All messages made available as part of this discussion group (including any bulletin boards and chat rooms) and any opinions, advice, statements or other information contained in any messages posted or transmitted by any third party are the responsibility of the author of that message and not of CSSForum.com.pk (unless CSSForum.com.pk is specifically identified as the author of the message). The fact that a particular message is posted on or transmitted using this web site does not mean that CSSForum has endorsed that message in any way or verified the accuracy, completeness or usefulness of any message. We encourage visitors to the forum to report any objectionable message in site feedback. This forum is not monitored 24/7.

Sponsors: ArgusVision   vBulletin, Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.