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 ⁿP_r 

1. ⁿP_r = n! / (n-r)!

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

3. ⁿP_n = n!

Combination

1.  ⁿC_r = n!/ r! × (n-r)!  
2.  ⁿC₀ = 1
3.  ⁿC_n = 1
4.  ⁿC_r =  ⁿCn - r 
5.  ⁿC_a =  ⁿC_b => a = b => a+b = n
6. ⁿC₀ + ⁿC₁+ ⁿC₂+ ⁿC₃+ ...............+ ⁿC_n = 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

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 ⁿP_r = ⁿC_r  × 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.

 ⁿC_r = n!/ r! × (n-r)!  

 ⁴C₃ = 4!/3! × ( 4- 3)! 

 ⁴C₃ = 4!/3! × 1! 

 ⁴C₃ = 4!/3! × 1!

 ⁴C₃ = 4

Or

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.

ⁿP_r = n! / (n-r)!

ⁿP_r = 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 :