**Permutation**

- In mathematics, permutation is nothing but the combination which is ordered.
- If we have n objects and out of which we have to arrange r objects where order is considered is given by permutation which has formula,

^{n}P_{r} = n! / (n – r)!

- Combination is given by,
^{n}C_{r}= n! / r! (n – r)! - Now, the relation between permutation and combination is given by,

^{n}**C _{r} = n! / r! (n – r)! = ^{n}P_{r} / r!**

- Permutation is used for arranging letters, numbers or data where order of arrangement is considered.

**For example:**

**1.) If the word CHANCE is given, we have to find the number of different ways in which the letters of the word to be arranged.**

Ans:

- In the word CHANCE, there are total 6 letters.
- But the letter C is repeating two times.
- Hence, the number of possible different arrangements will be given by,

(Total number of letters)! / (number of repeating letters)!= 6! / 2! = 720/ 2 = 360

- Thus, we can arrange the letters of the word CHANCE in 360 different ways.

**2) If the word is given CHAIR and we have to find the number of possible different ways of arranging letters of that word.**

Ans:

- Here in word CHAIR only 5 different letters are present.
- Hence the number of different ways of arranging letters of the word CHAIR will be given by,
- (Total number of different letters)! / (number or repeated letters)! = 5! / 0! = 120/ 1 = 120

Thus, the number of possible different ways of arranging letters of the word CHAIR will be 120.