Distinguishable Permutation

 

The number of permutation of n objects where there are n₁ repeated items, n₂ repeated items, ... n_k repeated items.

P = n!/n₁!*n₂!...n_k!

Where:

P is the total number of permutations

n is the total number of objects in the set

„n₁, n₂,..n_k is the total number of repeated items/objects

Sample Problems: Find the Permutation of the letters of the following:

1. MANILA

2. PHILIPPINES

Solution:

1. MANILA

Given:

P = ?; n = 6; n₁ = 2

Formula:

P = n!/(n₁!*n₂!*...n_k!)

Solution:

P = 6!/2! = 6*5*4*3*2!/2! = 180

2. PHILIPPINES

Given:

P = ?; n = 11; n₁ = 3; n₂ = 3

Formula:

P = n!/(n₁!*n₂!*...n_k!)

Solution:

P = 11!/3!*3! 

P = 11*10*9*8*7*6*5*4*3!/3*2*1*3!

P = 739,200