# Permutations and Combinations Basics

Friends, in this post we shall discuss about another important topic of Aptitude Section, Permutations and Combinations. Lets start with definitions. Ofcourse all of you might have already tried to learn the standard definitions of Permutations and Combinations and almost fed up with them.  So now we are not going to repeat those technical definitions again. Lets try to understand in simple words, what is permutation and what is combination.

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
ACD   BCD    CBD    DBC

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 ?
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.
Now lets have a look at the mathematical formula for Combinations..

 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.

1. hello....
After 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

1. You just took r instead of r! in the denominator Rashmi...

the solution will be like

(4X3X2X1)/(3X2X1)(1) = 4

hope you got it now...

2. In Denominator formula is factorial r multiple by factorial (n-r). So in denominator fact. of 3 * fact. (4-3). Hope u will understand.

3. Its not "3" in denominator
Its 3!
So (4*3*2*1)/(3*2*1)*(4-3)= 4

4. your way of calculation is wrong
C(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.

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1. We don't delete any links friend. If you encounter any deleted link, then please let us know. we will update :)

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6. having problem in understanding this topic. :(

7. 1/1*2 + 1/2*3 + 1/3*4 + ..... + 1/9*10
What may be d right Answer.
Optios are 1) 11/10, 2) 7/10,3) 9/10, 4)1. How can solve this ??

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