Tuesday, 4 July 2017

Permutations and Combinations II: Basic Permutations and Combinations Questions for Bank Exams

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

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.
Permutations and Combinations Questions
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 2:
Number of ways in which these 5 people can stand in a row are
Permutations and Combinations Questions
Step 3:
5p5 = [5!/ (5 – 5)!] 
5p5 =[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 2: 
Permutations and Combinations Questions
Step 3: 
6pr = 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- 
Permutations and Combinations Questions
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 
Permutations and Combinations Questions
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 
Permutations and Combinations Questions
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:
Permutations and Combinations Questions
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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Permutations and Combinations Questions
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