Permutation and Combination

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)

= 10³

= 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) => 5³

=> 5*5*5

=> 125

Permutation without Repetition

ⁿP_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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