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

The 6 letters word YELLOW can be arranged in 360 distinct ways. The below detailed information shows how to find how many ways are there to order the letters YELLOW and how it is being calculated in the real world problems.

**Distinguishable Ways to Arrange the Word YELLOW**

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 YELLOW be arranged.

__Objective:__

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

__Step by step workout:__

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

__Formula:__

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

__Input parameters and values:__

Total number of letters in YELLOW:

n = 6

Distinct subsets:

Subsets : Y = 1; E = 1; L = 2; O = 1; W = 1;

Subsets' count:

n_{1}(Y) = 1, n_{2}(E) = 1, n_{3}(L) = 2, n_{4}(O) = 1, n_{5}(W) = 1

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

nPr = 6!/(1! 1! 2! 1! 1! )

= 1 x 2 x 3 x 4 x 5 x 6/{(1) (1) (1 x 2) (1) (1)}

= 720/2

= 360

nPr of word YELLOW = 360

Hence,

The letters of the word YELLOW can be arranged in 360 distinct ways.

Apart from the word YELLOW, 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.