# How many Ways to Arrange 10 Letters Word PROSPERITY?

907200 is the number of ways to arrange 10 letters (alphabets) word "PROSPERITY" 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 10 alphabets or letters of a "PROSPERITY".
The partial possible number of ways to arrange the letters of word "PROSPERITY" are ROIPSRTPEY, YRPOTPIERS, ROPYPTISER, EORTYPSRPI, IOEPPSYRRT, PORRTSPEYI, TEORYPISPR, PESIYRTPRO, YSEPIRTPRO, TIRYSOPREP. Refresh the page to get the another set of partial arrangements.

## Distinct Ways to Arrange Word PROSPERITY - Workout

The below workout is the step by step procedure to find how many number of distinct ways to arrange the 10 letters (alphabets) of word "PROSPERITY". Users may use any other word by changing the word "PROSPERITY" 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 "PROSPERITY"

n = 10

Subsets : P = 2; R = 2; O = 1; S = 1; E = 1; I = 1; T = 1; Y = 1;

n_{1}(P) = 2, n_{2}(R) = 2, n_{3}(O) = 1, n_{4}(S) = 1, n_{5}(E) = 1, n_{6}(I) = 1, n_{7}(T) = 1, n_{8}(Y) = 1

step 2 Apply the input parameter values in the nPr formula

= 10!/(2! 2! 1! 1! 1! 1! 1! 1! )

= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10/{(1 x 2) (1 x 2) (1) (1) (1) (1) (1) (1)}

= 3628800/4

= 907200

In 907200 distinct ways, the letters of word "PROSPERITY" can be arranged.