# How many Ways to Arrange 9 Letters Word FRACTIONS?

362880 is the number of ways to arrange 9 letters (alphabets) word "FRACTIONS" by using *Permutations (nPr)* formula. Users may refer the below workout with step by step procedure to understand how to estimate how many number of ways to arrange 9 alphabets or letters of a "FRACTIONS".
The partial possible number of ways to arrange the letters of word "FRACTIONS" are NITRFACOS, IASONRFTC, SCFTIONAR, AORCITNSF, NFITCSROA, OITNACRFS, NATFOSRCI, STOICANRF, STNARIOCF, CFATRINOS. Refresh the page to get the another set of partial arrangements.

## Distinct Ways to Arrange Word FRACTIONS - Workout

The below workout is the step by step procedure to find how many number of distinct ways to arrange the 9 letters (alphabets) of word "FRACTIONS". Users may use any other word by changing the word "FRACTIONS" to find the total number of distinct ways to arrange different words.

__Step by step workout__

step 1 Address the formula, input parameters and values

__Formula:__

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

__Input Parameters & Values:__

Total number of alphabets (n) & subsets (n1, n2, . . nk) in the word "FRACTIONS"

n = 9

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

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 input parameter values in the nPr formula

= 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

In 362880 distinct ways, the letters of word "FRACTIONS" can be arranged.