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Permutation and Combination - Introduction and Examples (Part - 1) | Quantitative Aptitude for Competitive Examinations - Banking Exams PDF Download

Permutation

Permutation is basically called as a arrangement where order does matters.Here we need to arrange the digits , numbers , alphabets, colors and letters taking some or all at a time.It is represented as nPr 

Permutation and Combination - Introduction and Examples (Part - 1) | Quantitative Aptitude for Competitive Examinations - Banking Exams

Permutation and Combination - Introduction and Examples (Part - 1) | Quantitative Aptitude for Competitive Examinations - Banking Exams

1. nPr = n! / (n-r)!

2. If from the total set of n numbers p is of one kind and q ,r are others respectively then nPr = n! / p! × q! × r!.

3. nPn = n!

Combination

Permutation and Combination - Introduction and Examples (Part - 1) | Quantitative Aptitude for Competitive Examinations - Banking Exams

Permutation and Combination - Introduction and Examples (Part - 1) | Quantitative Aptitude for Competitive Examinations - Banking Exams

  1.  nCr = n!/ r! × (n-r)!  
  2.  nC0 = 1
  3.  nCn = 1
  4.  nCr =  nCn - r 
  5.  nCa =  nCb => a = b => a+b = n
  6. nC0nC1nC2nC3+ ...............+ nC= 2n

Permutation vs Combination

In both the things main difference is of order .In permutation order matters while in combination it does not.

Basic Difference :

  1. order
  2. arrange or choose 
  3. number of permutation > number of combination

Permutation and Combination - Introduction and Examples (Part - 1) | Quantitative Aptitude for Competitive Examinations - Banking Exams

Permutation and Combination - Introduction and Examples (Part - 1) | Quantitative Aptitude for Competitive Examinations - Banking Exams

Permutation and Combination - Introduction and Examples (Part - 1) | Quantitative Aptitude for Competitive Examinations - Banking Exams

In Arrangements we have,

Total no. of arrangements = total no. of groups or selection × r!

where r is the no. of objects in each group or selection. So nPrnCr  × r!

Questions :

1. How many triangles can be formed with four points (A,B,C & D) in a plane ? It is given that no three points are col-linear(not comes in straight line).From the three points A,B and C have only one triangle with these points.

Sol:

Here in this question  , Order of digit does not matter so it is a combination.

 nCr = n!/ r! × (n-r)!  

 4C= 4!/3! × ( 4- 3)! 

 4C= 4!/3! × 1! 

 4C= 4!/3! × 1!

 4C= 4

Or

Permutation and Combination - Introduction and Examples (Part - 1) | Quantitative Aptitude for Competitive Examinations - Banking Exams
Permutation and Combination - Introduction and Examples (Part - 1) | Quantitative Aptitude for Competitive Examinations - Banking Exams

2. How many number plates of 3 digit can be formed with four digits 1,2,3 and 4 ?

Sol:

Here, the order of arrangement of digits does matter.

nPr = n! / (n-r)!

nPr = 4! / (4-3)!

4P3 = 4! / 1!

 4P3 = 4!

 4P3 = 24

Factorial Notation

To solve problem like this you must have the knowledge of factorial.Factorial is represented as like " ! ".The Factorial notation is :

Permutation and Combination - Introduction and Examples (Part - 1) | Quantitative Aptitude for Competitive Examinations - Banking Exams

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FAQs on Permutation and Combination - Introduction and Examples (Part - 1) - Quantitative Aptitude for Competitive Examinations - Banking Exams

1. What is the difference between permutation and combination?
Ans. Permutation and combination are both methods used to count the number of possible outcomes in a given situation. The main difference between them lies in their approach. Permutation is concerned with the arrangement of objects in a particular order, while combination focuses on selecting objects without considering their order.
2. How do you calculate the number of permutations?
Ans. To calculate the number of permutations, you multiply the total number of objects by one less than the previous number, and so on, until you reach the desired number of objects. For example, if you have 5 objects and want to arrange them in 3 positions, the calculation would be 5 * 4 * 3 = 60 permutations.
3. How do you calculate the number of combinations?
Ans. The number of combinations can be calculated using the formula nCr = n! / (r!(n-r)!), where n represents the total number of objects and r represents the number of objects being selected at a time. The exclamation mark denotes the factorial function, which means multiplying all positive whole numbers from 1 to the given number.
4. Can you give an example of permutation?
Ans. Sure! Let's say you have 3 different colored balls (red, blue, and green) and you want to arrange them in a row. The possible permutations would be: red-blue-green, red-green-blue, blue-red-green, blue-green-red, green-red-blue, and green-blue-red. In total, there are 6 different permutations.
5. Can you give an example of combination?
Ans. Of course! Let's say you have 5 different books on a shelf and you want to select 2 books to read. The possible combinations would be: book 1 and book 2, book 1 and book 3, book 1 and book 4, book 1 and book 5, book 2 and book 3, book 2 and book 4, book 2 and book 5, book 3 and book 4, book 3 and book 5, and book 4 and book 5. In total, there are 10 different combinations.
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