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

The 10 letters word PROSPERITY can be arranged in 907200 distinct ways. The below detailed information shows how to find how many ways are there to order the letters PROSPERITY and how it is being calculated in the real world problems.

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Distinguishable Ways to Arrange the Word PROSPERITY
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 PROSPERITY be arranged.

Objective:
Find how many distinguishable ways are there to order the letters in the word PROSPERITY.

Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters PROSPERITY.
Formula:
nPr =n!/(n1! n2! . . . nr!)

Input parameters and values:
Total number of letters in PROSPERITY:
n = 10

Distinct subsets:
Subsets : P = 2; R = 2; O = 1; S = 1; E = 1; I = 1; T = 1; Y = 1;
Subsets' count:
n1(P) = 2, n2(R) = 2, n3(O) = 1, n4(S) = 1, n5(E) = 1, n6(I) = 1, n7(T) = 1, n8(Y) = 1

step 2 Apply the values extracted from the word PROSPERITY in the (nPr) permutations equation
nPr = 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
nPr of word PROSPERITY = 907200

Hence,
The letters of the word PROSPERITY can be arranged in 907200 distinct ways.

Apart from the word PROSPERITY, 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. 