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Best explanation to understand and solve the permutation and combination

This aptitude section has the aptitude questions based on the topic PERMUTATION AND COMBINATION. This is one of the important topics in arithmetic aptitude.

You will have many questions based on this topic in many bank exams and entrance exams. In interviews also you may have questions based on permutation  and combination.

This article will help you to know more about the formulas and tricks to solve these problems in your exams.

Moreover, we also have a set of aptitude questions which will help you to practice for your exams.

Read the article and know more about permutation and combination.

What is permutation?

In mathematics, permutation refers to the act of arranging the members of the given set in an order or a sequence.  Or, if the set is already in an order or sequence, rearranging its element is called permutation. 

For example:

Let we have three letters a, b, and c. We have to arrange these two letters at a time. In this case, the permutations of the given two letters are  ab, ba, bc, cb, ac, and ca.

If we have to arrange all letters (a,b,c) simultaneously, the permutation would be: abc, acb, bac, bca, cab, and cba.

What is called combination?

In mathematics, permutation and combination are studied together because they both have the similar concept.

Combination does not involve in ordered arrangement of the element. It is only the collection of any set of the elements.

For example:

If we have a set of three letters like A, B, and C, We might ask how many ways we can select 2 letters from that set. The complete possible list will be only three, that is  AB, BC and AC.

There is no need of arranging the elements in order. 

What is the difference between permutation and combination?

The only difference between permutation and combination is that ordered arrangement of the given set of elements.

Permutation focus on the sequential arrangement of the given elements where as combination does not. 

What is factorial?

In mathematics, factorial is the function that is applicable for natural numbers above zero.

It is the function of multiplying all the natural number to the given number which are smaller that the number.

The symbol for factorial is !. 

For example: we can represent the factorial of 2 as 2!

What are the formulas to solve permutation and combination aptitude?

FACTORIAL:

Formula for the factorial of n is given by

n! (Factorial of n) = n (n-1) (n-2)….1

For example:

The factorial of 3:

3! = 3*2*1 = 6

PERMUTATION:

Formula for calculating the number of possible permutations of ‘r’ things, from a set of ‘n’ at a time is as follows

nPr = n(n – 1)(n – 2)(n – 3)… (n – r + 1) = n! / (n – r)! 

For example:              

8P3 = 8! / (8 – 3)! = ( 8 x 7 x 6 x 5 ) / 5 = 8 x 7 x 6 = 336

The number of permutations or arrangements of n things at a time = n! (Factorial of n). 

That is n = 3, so 3! = 3*2*1 = 6 (the number of permutations = 6)

COMBINATION:

Formula for calculating the possible combination for ‘r’ things, from a set of ‘n’ objects at a time is as follows

nCr = n ! / r! (n – r) = ( n(n – 1) (n – 2) … (n – r + 1)) / r!

Note:

i) nCn = 1

ii) nC0 = 1

iii) nCr = nC(n-r)

For example: 

7C5 = 7C(7-5) = 7C2 =(7 x 6) / (2 x 1) = 21

Points to remember

When the number of things is x, y, and z then the number of combinations taking two at a time will be xy, yz, and zx.

(NOTE: yx and xy are same in a combination. But are not the same in permutation). 

The combination of all things at a time is xyz.

These are the important terms and formulas that should be known by you before appearing for your examination.

This will be very useful for you to learn for your exams and you may take up the given aptitude test in our website and can increase your speed and ability in solving the problems.