# How Many Ways are There to Order the Letters of Word PEACE?

The 5 letters word PEACE can be arranged in 60 distinct ways. The below detailed information shows how to find how many ways are there to order the letters PEACE and how it is being calculated in the real world problems.

**Distinguishable Ways to Arrange the Word PEACE**

The below step by step work generated by the word permutations calculator shows how to find how many different ways can the letters of the word PEACE be arranged.

__Objective:__

Find how many distinguishable ways are there to order the letters in the word PEACE.

__Step by step workout:__

step 1 Address the formula, input parameters and values to find how many ways are there to order the letters PEACE.

__Formula:__

nPr =n!/(n1! n2! . . . nr!)

__Input parameters and values:__

Total number of letters in PEACE:

n = 5

Distinct subsets:

Subsets : P = 1; E = 2; A = 1; C = 1;

Subsets' count:

n_{1}(P) = 1, n_{2}(E) = 2, n_{3}(A) = 1, n_{4}(C) = 1

step 2 Apply the values extracted from the word PEACE in the (nPr) permutations equation

nPr = 5!/(1! 2! 1! 1! )

= 1 x 2 x 3 x 4 x 5/{(1) (1 x 2) (1) (1)}

= 120/2

= 60

nPr of word PEACE = 60

Hence,

The letters of the word PEACE can be arranged in 60 distinct ways.

Apart from the word PEACE, you may try different words with various lengths with or without repetition of letters to observe how it affects the nPr word permutation calculation to find how many ways the letters in the given word can be arranged.