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

The 3 letters word ICE can be arranged in 6 distinct ways. The below detailed information shows how to find how many ways are there to order the letters ICE and how it is being calculated in the real world problems.

**Distinguishable Ways to Arrange the Word ICE**

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 ICE be arranged.

__Objective:__

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

__Step by step workout:__

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

__Formula:__

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

__Input parameters and values:__

Total number of letters in ICE:

n = 3

Distinct subsets:

Subsets : I = 1; C = 1; E = 1;

Subsets' count:

n_{1}(I) = 1, n_{2}(C) = 1, n_{3}(E) = 1

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

nPr = 3!/(1! 1! 1! )

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

= 6/1

= 6

nPr of word ICE = 6

Hence,

The letters of the word ICE can be arranged in 6 distinct ways.

Apart from the word ICE, 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.