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# Permutation And Combination Question and Answer with Explanation

## 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.

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

### 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.

1.

In how many different ways can the letters of the word ' PROVIDE' be arranged so that the vowels always come together?

2.

In the word ' INVESTS ' calculate how many ways can the letters be arranged?

3.

Evaluate 5! ?

4.

Find the number of permutations of the letters of the word SLEEP.

5.

If nC9 = nC8, find nC17

6.

How many words we will get from all the letters of the word ' Yourself' so that the vowels in the word always come together ?

7.

Calculate the number of words we can get from the letters of the word 'ANGEL' so that the vowels are never together.

8.

In how many ways the number of words can be formed from the word 'PERSONAL' so that the vowels are always together?

9.

Find the value of (n+4)!/(n+7)!

10.

Out of 12 members of a club, 8 are senior members. The club plans for 8 potential members. If exactly 6 members of committee must seniors, how many committees are possible.

11.

How many number of words can be formed by using all the letters of the word 'ACTOR' using each letter exactly once and it is not necessary that the word which formed all have meaning , the words will be with or without meaning.

12.

How many number of ways material can be arranged, such that all vowels are together.

13.

In how many different ways can the letters PROTEIN can be arranged so that all vowels always come together.

14.

In how many ways the word ' caste' is arranged, using all letters exactly once.?

15.

In how many number of ways, the word 'IMPERIAL' be arranged, such that all vowels lie together.

16. how many 4-digit number can be formed from the digits 2,4,5,6,8 and 9 which are divisible by 5 and none of the digits is repeated?
17. A box contain 2 blue balls, 3 green balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one red ball is to be drawn?
18. In a party, there are 50 people.Each person shakes their with every other person.How many handshakes take place?
19. How many different 4-letter words can be formed using the letter of the word CONSTITUTION such it starts with C ends with N?
20. From a group of 6 men and 8 women, six persons are to be selected to from a committee such that there are at least 2 men and 2 women in the committee. In how many ways can it be done?
21. In how many ways can 5 letters be posted in 4 postboxes if each postbox can contain any number of letters?
22. In how many ways can four cards of different suits having the same value be selected from a standard pack of cards?
23. Find the number of possible ways in which 8 students can be divided into 4 equal teams to take part in an inter-school competition.
24. In how many ways can the letter of the word EDUCATE be rearranged so that the two Es do not appear together?
25. A family of 10 people travel in two cars of which one can seat 6 and the other only 5 In how many ways can they travel?
26. Find the number of permutations from the letters of the word 'SPECIAL' so that the vowels always come together?
27. How many different permutations can be made out of the letters of the word : abbreviations