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) = nr
= 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
nPr = 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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