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

The 9 letters word FRACTIONS can be arranged in 362880 distinct ways. The below detailed information shows how to find how many ways are there to order the letters FRACTIONS and how it is being calculated in the real world problems.

**Distinguishable Ways to Arrange the Word FRACTIONS**

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 FRACTIONS be arranged.

__Objective:__

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

__Step by step workout:__

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

__Formula:__

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

__Input parameters and values:__

Total number of letters in FRACTIONS:

n = 9

Distinct subsets:

Subsets : F = 1; R = 1; A = 1; C = 1; T = 1; I = 1; O = 1; N = 1; S = 1;

Subsets' count:

n_{1}(F) = 1, n_{2}(R) = 1, n_{3}(A) = 1, n_{4}(C) = 1, n_{5}(T) = 1, n_{6}(I) = 1, n_{7}(O) = 1, n_{8}(N) = 1, n_{9}(S) = 1

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

nPr = 9!/(1! 1! 1! 1! 1! 1! 1! 1! 1! )

= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9/{(1) (1) (1) (1) (1) (1) (1) (1) (1)}

= 362880/1

= 362880

nPr of word FRACTIONS = 362880

Hence,

The letters of the word FRACTIONS can be arranged in 362880 distinct ways.

Apart from the word FRACTIONS, 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.