Question

Find the number of unique permutations of the letters in the word: ONGOING

Answer 1

The Number of unique permutation is 6,615

Explanation:

This particular permutation deals with words that have repeated letters.

Given word = "ONGOING"

the formula for the permutation is

`= (n!)/(mA! mB!.....mZ!)`

where n is the amount of letters in the word, and m A , m B , ... , m Z are the occurrences of repeated letters in the word. Each m equals the amount of times the letter appears in the word.

So in the word "ONGOING"

n= 7

mO= 2

mN= 2

mG=2

`permutations = (7!)/(2!2!2!) \\\\permutations= (7*6*5*4*3*2*1)/((2*1)*(2*1)*(2*1))`

`permutations= (52920)/(8) \\permutation = 6,615`