Question

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

Answer 1

Answer:

The Number of unique permutation is  6,615

Step-by-step explanation:

  This particular permutation  deals with words that have repeated letters.

Given word = "ONGOING"

the formula for the permutation is

$= \frac{n!}{mA! mB!.....mZ!}$

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

$permutations = \frac{7!}{2!2!2!} \\\\permutations= \frac{7*6*5*4*3*2*1}{(2*1)*(2*1)*(2*1)}$

$permutations= \frac{52920}{8} \\permutation = 6,615$