In Permutation order does matter but in Combination order doesn’t matter.

A permutation is an ordered combination.

There are two types of permutation

**Permutation with Repetition**

- When a thing has n different types, we have n choices each time
- Choosing 3 things =>
**n * n * n**

**Example** 1: We have 10 numbers & we have to select only three of them

**Solution:**

n*n*n*……………….(r times) =

n^{r}

= 10 * 10 * 10 (3 times)

= 10^{3}

= 1000 permutations

**Example** 2: How many 3 letter words with or without meaning can be formed out of letters of word **SMOKE** when **repetition is allowed**?

**Solution:**

Here SMOKE has 5 alphabets,

So n = 5 & we have to arrange in r=3 letter words

Permutation (When repetition is allowed) => 5^{3}

=> 5*5*5

=> 125

**Permutation without Repetition**

^{n}P_{r}= n! / (n−r)!

**Example** 1: How many **three **letter words with or without meaning can be formed out of the letters of the word **SWING **when **repetition **of letters is** not allowed**?

**Solution**

Here n=5 (SWING has 5 letters)

we have to frame 3 letter words (r)

So permutation p(n,r) = 5! / (5-3)!

= 5! / 2!

= 5 * 4 * 3 * 2 * 1 / 2*1

= 5 * 4 * 3

= 60

**Example 2:** Find the number of words that can be formed with letters of word INDIA

**Solution**:

INDIA => 5 Letters

‘I’ comes => twice

When a letter comes more than once in a word, we divide the factorial of the number of all letters in the word by the number of occurrences of each letter

Therefore, INDIA = 5!/2!

= 5*4*3*2*1 /2*1

= 5*4*3

= 60

**Important Permutation Formula**

1! = 1

0! = 1

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