Permutation and Combination

Permutation : It is the different arrangements of a given number of elements taken one by one, or some, or all at a time.

For example, if we have two elements A and B, then there are two possible arrangements, AB and BA.

1.Use permutations if a problem calls for the number of arrangements of objects and different orders are to be counted. 

2.Use combinations if a problem calls for the number of ways of selecting objects and the order of selection is not to be counted.

Permutation is an arrangement of a group of objects where the order does  matter.

 Let’s Understand this by few Examples.

Let’s say, I have to choose an alphabet. In how many ways can I chose?

The ans is 26 ways, because there are 26 alphabets.

•In how many ways can I chose a vowel?

    Ans is 5 ways, because there are 5 vowels only.

•In how many ways can I chose a consonant?

   Ans is 21 ways, because there are 21 consonants only.

The formula of permutations of 'n’ different things taken 'r' at a time is

          nPr = n! / (n-r)!

Means to say, if we have 3 letters (A, B, C) and we take 2 letters

(like AB, AC, etc.) at a time 

ways = 3P2 = 3!/(3-2)! = 3!/1! = 6 ways

•We can make AB, AC, BA, BC, CA, CB = 6 ways.

 This is called permutation

Know About Factorials:

n! = n * (n-1) * (n-2) * (n-3) ………..* 1

5! = 5 x 4 x 3 x 2 x 1 =120

Below factorials need to keep in mind:

0! = 1          7!=5040

1! = 1          8! =40320

2!= 2

3! = 6

4! = 24

5! =120

6! =720

What is the value of ⁿC₄, if ⁿC₆ = ⁿC₅?

a) 330                           b) 440                           c) 360                           d) 420

Solution:

If  ⁿC_r = ⁿC_s , then either r = s (or) n = r + s

Here, r = 6 and s = 5      =>        n = 6 + 5 = 11

⸫ ⁿC₄ = ¹¹C₄ = (11 × 10 × 9 × 8) / 4! = 330.

Answer: a

Click below for more