How Many Ways are There to Order the Letters of Word CORPORATION?
The 11 letters word CORPORATION can be arranged in 3326400 distinct ways. The below detailed information shows how to find how many ways are there to order the letters CORPORATION and how it is being calculated in the real world problems.
Distinguishable Ways to Arrange the Word CORPORATION
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 CORPORATION be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word CORPORATION.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters CORPORATION.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in CORPORATION:
n = 11
Distinct subsets:
Subsets : C = 1; O = 3; R = 2; P = 1; A = 1; T = 1; I = 1; N = 1;
Subsets' count:
n1(C) = 1, n2(O) = 3, n3(R) = 2, n4(P) = 1, n5(A) = 1, n6(T) = 1, n7(I) = 1, n8(N) = 1
step 2 Apply the values extracted from the word CORPORATION in the (nPr) permutations equation
nPr = 11!/(1! 3! 2! 1! 1! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11/{(1) (1 x 2 x 3) (1 x 2) (1) (1) (1) (1) (1)}
= 39916800/12
= 3326400
nPr of word CORPORATION = 3326400
Hence,
The letters of the word CORPORATION can be arranged in 3326400 distinct ways.
Apart from the word CORPORATION, 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.
