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

The 5 letters word LAKES can be arranged in 120 distinct ways. The below detailed information shows how to find how many ways are there to order the letters LAKES and how it is being calculated in the real world problems.

**Distinguishable Ways to Arrange the Word LAKES**

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 LAKES be arranged.

__Objective:__

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

__Step by step workout:__

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

__Formula:__

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

__Input parameters and values:__

Total number of letters in LAKES:

n = 5

Distinct subsets:

Subsets : L = 1; A = 1; K = 1; E = 1; S = 1;

Subsets' count:

n_{1}(L) = 1, n_{2}(A) = 1, n_{3}(K) = 1, n_{4}(E) = 1, n_{5}(S) = 1

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

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

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

= 120/1

= 120

nPr of word LAKES = 120

Hence,

The letters of the word LAKES can be arranged in 120 distinct ways.

Apart from the word LAKES, 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.