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In my school days I have a BIG confusion on which one is permutation and which one is combination. Then my uncle told me a simple technique to remember them without confusion.
He said, permutation is always complicated than combination
In simple words
- If the order is important, it is a Permutation.
- If the order is not important, it is a Combination.
Still confused ? lets discuss with examples.
Permutation :
Assume that I have 4 letters (A, B, C and D). Now if anybody asks me to write down all the permutations of 3 of these letters.....
ABC BAC CAB DAB
ACB BCA CBA DBA
ABD BAD CAD DAC
ADB BDA CDA DCA
ACD BCD CBD DBC
ADC BDC CDB DCB
ACB BCA CBA DBA
ABD BAD CAD DAC
ADB BDA CDA DCA
ACD BCD CBD DBC
ADC BDC CDB DCB
So, there are 24 permutations in total. Here the order is important. In other words ACB is different, BCA is different, CBA is different and ABC is different (even-though they all are formed with same group letters).
Combination :
As we have already discussed, the collection of letters is important here, not the order. That means, if you have ABC in your set that's enough. So you cant claim ABC, ACB, BAC, BCA, CAB, CBA... for combinations. These all are 1 combination of letters A, B and C.
So, from the given 4 letters (A, B, C and D), You can write the combination of 3 of those letters
ABC ABD ACD BCD
hope you have got the basic concept now.
Now lets have a look at the technical side, before going to calculate Permutations and Combinations, you should know the word Factorial.
Factorial : The factorial of a number, represented by n!, is the product of the natural numbers up to and including n
In simple words, the Factorial of the number n is the number of ways that the n elements of a group can be ordered.
So, if somebody ask you a question, how many different ways six people can sit at a table with six chairs,
you should say them its 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.
Note : We treat 0! as 1
How to Calculate Permutations ?
Factorial : The factorial of a number, represented by n!, is the product of the natural numbers up to and including n
In simple words, the Factorial of the number n is the number of ways that the n elements of a group can be ordered.
So, if somebody ask you a question, how many different ways six people can sit at a table with six chairs,
you should say them its 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.
Note : We treat 0! as 1
How to Calculate Permutations ?
There is a simple formula for calculating permutations.
Number of all permutations of n items, taken r at a time, is given by:
nPr = n(n - 1)(n - 2) ... (n - r + 1)
=
n above case n is 4 and r is 3
So, nPr = P(n,r) = 24
How to Calculate Combinations ?
Important Note : To calculate combinations,
- First you should calculate all the equivalent permutations.
- Later you should correct this list by cutting out duplicates / repetitions.
nCr = | n! | = | n(n - 1)(n - 2) ... ... r | . |
(r!)(n - r!) | r! |
n above case n is 4 and r is 3, so
nCr = C(n,r) = 4
That's all for now friends. In our next post we shall discuss some practice problems on Permutations and Combinations.
Home Work :
Before going to leave, you have a small Home Work kind of Stuff here. The below pdf file consists of some basic shortcut techniques on Permutations and Combinations with some simple examples. Just download this pdf file and prepare well. It will help you getting good idea on the concepts and approach.
Download pdf file Permutations and Combinations shortcut techniques from here
hello....
ReplyDeleteAfter solving the Combination ans is C(n,r) is 8 in the above example... how it came 4....???
if n-4,r=3
n! / (r!)(n-r!)
4*3*2*1 / (3)*(4-3) = 8
You just took r instead of r! in the denominator Rashmi...
Deletethe solution will be like
(4X3X2X1)/(3X2X1)(1) = 4
hope you got it now...
In Denominator formula is factorial r multiple by factorial (n-r). So in denominator fact. of 3 * fact. (4-3). Hope u will understand.
DeleteIts not "3" in denominator
DeleteIts 3!
So (4*3*2*1)/(3*2*1)*(4-3)= 4
your way of calculation is wrong
DeleteC(n,r)= n!/(r!)*(n-r)
Where n=4, r=3
then combination is
= 4!/3!*(4-3)
4*3*2*1/3*2*1*1
=24/6
Ans is 4.
Dear mam,u r really giving vaulable information to us bt am requesting u that dnt delete these links plz bcoz its useful 4us in future hope u understand...thnks
ReplyDeleteWe don't delete any links friend. If you encounter any deleted link, then please let us know. we will update :)
DeleteVery nice
ReplyDeleteso nice of u mam :)
ReplyDeleteso nice of u mam thank u for ur valuable information
ReplyDeletehaving problem in understanding this topic. :(
ReplyDelete1/1*2 + 1/2*3 + 1/3*4 + ..... + 1/9*10
ReplyDeleteWhat may be d right Answer.
Optios are 1) 11/10, 2) 7/10,3) 9/10, 4)1. How can solve this ??
9/10
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ReplyDeletethank u for ur nice work
ReplyDelete