Unique Ways to Arrange Alphabets 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 arranged in the real world problems.
Unique Ways to Arrange the Word PROSPERITY
The below step by step work generated by this permutation calculator shows how to find how many different ways, the letters of the word PROSPERITY can 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.
