**In this post, we will discuss basic Permutations and Combinations Questions which will help you save time in Bank Exams.**

No matter what, Permutations and Combinations Questions always make their way in Bank Exams. Though these Questions appear to be complex and confusing, they can be easily solved by using permutations and combinations formulas. In this post, we have discussed few basic and advanced permutations and combinations questions which will help you save time in Bank Exams.

Before moving further, quickly review the basics of the topic and important permutations and combinations formulas to solve permutations and combinations questions easily.

**Basic Permutations and Combinations Questions**

**Example 1: Permutations and Combinations Questions**

**Question:**In how many different ways can 5 people stand in a row for a photograph?

**Solution:**

**Step 1:**

Let us assume 5 persons to be as A, B, C, D and E

**Step 3:**

5

5

5! = 120

Therefore, there are 120 different ways in which 5 people can stand in a row for a photograph.

_{p5}= [5!/ (5 – 5)!]5

_{p5}=[5!/ (0!)] (5! = 1 x 2 x 3 x 4 x 5) (0! = 1)5! = 120

Therefore, there are 120 different ways in which 5 people can stand in a row for a photograph.

**Basic Permutations and Combinations Questions**

**Example 2: Permutations and Combinations Questions**

**Question:**How many different words can be formed using letters of the word “Banker?”

**Solution:**

**Step 1:**

We have 6 different letters i.e. B, A, N, K, E and R. we need to find different ways in which different words can be formed using these 6 letters.

**Step 3:**

6

_{pr}= 6! (6! = 1 x 2 x 3 x 4 x 5 x 6)

= 720

Therefore, 720 words can be formed using the 6 letters from BANKER.

**Advance Permutations and Combinations Questions**

The number of permutation of ‘n’ objects taken all at a time, where ‘p’ objects are similar to one type, ‘q’ objects are similar to the second type and ‘r’ objects are similar to the third type will be equal to-

**Advance Permutations and Combinations Questions**

**Example 1: Permutations and Combinations Questions**

**Question:**How many different words can be formed using the letters of the words?

**(i)**

**MIRROR**

**Solution:**

**Step 1:**

There are 6 letters in the words MIRROR.

Therefore, 6! words can be formed.

**Step 2:**

The letter R has been repeated 3 times. Therefore we need to divide 6! with 3! as

**Step 3:**

6!/ 3! = 720/ 6 = 120

Therefore, 120 words can be formed using the letters from the words MIRROR.

**(ii)BANANA**

**Solution:**

**Step 1:**

There are 6 letters in the words BANANA

Therefore, 6! words can be formed.

**Step 2:**

The letter A has been repeated 3 times and the letter N has been repeated 2 times. Therefore we need to divide 6! with 3! and 2! as

**Step 3:**

6!/ (3! x 2!) = 720/ (6 x 2) = 60

Therefore, 60 words can be formed using the letters from the words BANANA.

**Advance Permutations and Combinations Questions**

**Example 2: Permutations and Combinations Questions**

**Question:**A set of 12 books has 3 identical Quant books, 3 identical Reasoning books, 4 identical English books and 2 different books on General Awareness. In how many different ways can these 12 books be arranged on a bookshelf?

**Solution:**

**Step 1:**

n: Total number of books = 12

p: similar books on Quant = 3

q: similar books on Reasoning = 3

r: similar English books= 4

**Step 2:**

**Step 3:**

12! / (3! 3! 4!)

**Step 4:**

(12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)/(6 x 6 x 24)

= 554400

Therefore, there are 554400 ways in which books can be arranged on a bookshelf.

**Watch our expert faculty explain basic and advance permutations and combinations Questions**

**Permutations and Combinations Questions for Practice**

**Question:**How many different arrangements can be made by taking 4 letters of the word ENGLISH?

(1) 35 (2)210 (3)420 (4)840 (5) None of these

**Question:**How many ways can the letters of the word ‘APPLE’ can be arranged?

(1)72 (2)60 (3)24 (4)120 (5) None of these

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