 # Permutation Formula

Permutation formula is used to find the number of ways an object can be arranged without taking the order into consideration. To recall, when objects or symbols are arranged in different ways and order, it is known as permutation. Permutation can be done in two ways,

• Permutation with repetition: This method is used when we are asked to make different choices each time and have different objects.
• Permutation without Repetition: This method is used when we are asked to reduce 1 from the previous term for each time.

## Formulas for Permutations

The formulas for repetition and non-repetition permutation are as stated below:

Formulas to Calculate Permutation
Permuation Formula nPr = n! / (n−1)!
Permutation with Repetition Formula nPr = nr

### Solved Examples Using Permutation Formula

Question 1: Find the number of permutations if n = 9 and r = 2?

Solution:

Given n = 9 and r = 2

Permutation = nPr = n!/ (n−1)!

= (9 × 8 × 7 × 6 × 5 × 4)/2 = 181440

Question 2: Find how many ways you can rearrange the word “BANANA” all at a time?

Solution:

Given words: BANANA

Total number of letters in “BANANA” = 6

Total number of “A” in the word “BANANA” = 3

Total number of “N” in the word “BANANA” = 2

So, the permutation = (6!)/(3!2!) = (6 × 5 × 4 × 3!)/ (3!2!) = 60