This Article consist of most important ” Permutation and Combination Questions and Answers ” topic that are mostly asked in all competitive exams. We collected these questions from the students who appeared in exams. Now try to solve these questions.

## Permutation and Combination Questions and Answers

**Question : 1 ** In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions?

A. 32

B. 48

C. 36

D. 60

**Show Answer**

**Correct Answer : ** **C**

**Explanation : **

There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.

Let us mark these positions as under:

(1) (2) (3) (4) (5) (6)

Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.

Number of ways of arranging the vowels = 3P3 = 3! = 6.

Also, the 3 consonants can be arranged at the remaining 3 positions.

Number of ways of these arrangements = 3P3 = 3! = 6.

Total number of ways = (6 x 6) = 36

**Question : 2** How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

A. 5

B. 10

C. 15

D. 20

**Show Answer**

**Correct Answer : ** **D**

**Explanation : **

Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.

The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.

The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.

Required number of numbers = (1 x 5 x 4) = 20

**Question : 3** In how many ways can the letters of the word ‘LEADER’ be arranged?

A. 72

B. 144

C. 360

D. 720

**Show Answer**

**Correct Answer : ** **C**

**Explanation : **

The word ‘LEADER’ contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.

Required number of ways = 6!/(1!)(2!)(1!)(1!)(1!)

=360

**Question : 4 ** In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together?

A. 810

B. 1440

C. 2880

D. 50400

**Show Answer**

**Correct Answer : ** **D**

**Explanation : **

In the word ‘CORPORATION’, we treat the vowels OOAIO as one letter.

Thus, we have CRPRTN (OOAIO).

This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.

Number of ways arranging these letters = 7!/2! = 2520.

Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged

in 5!/3! = 20 ways.

Required number of ways = (2520 x 20) = 50400

**Question : 5 ** In how many different ways can the letters of the word ‘LEADING’ be arranged in such a way that the vowels always come together?

A. 360

B. 480

C. 720

D. 5040

**Show Answer**

**Correct Answer : ** **C**

**Explanation : **

The word ‘LEADING’ has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

Required number of ways = (120 x 6) = 720