Unique Ways to Arrange Alphabets of Word CALIFORNIA
The 10 letters word CALIFORNIA can be arranged in 907200 distinct ways. The below detailed information shows how to find how many ways are there to order the letters CALIFORNIA and how it is being arranged in the real world problems.
Unique Ways to Arrange the Word CALIFORNIA
The below step by step work generated by this permutation calculator shows how to find how many different ways, the letters of the word CALIFORNIA can be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word CALIFORNIA.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters CALIFORNIA.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in CALIFORNIA:
n = 10
Distinct subsets:
Subsets : C = 1; A = 2; L = 1; I = 2; F = 1; O = 1; R = 1; N = 1;
Subsets' count:
n1(C) = 1, n2(A) = 2, n3(L) = 1, n4(I) = 2, n5(F) = 1, n6(O) = 1, n7(R) = 1, n8(N) = 1
step 2 Apply the values extracted from the word CALIFORNIA in the (nPr) permutations equation
nPr = 10!/(1! 2! 1! 2! 1! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10/{(1) (1 x 2) (1) (1 x 2) (1) (1) (1) (1)}
= 3628800/4
= 907200
nPr of word CALIFORNIA = 907200
Hence,
The letters of the word CALIFORNIA can be arranged in 907200 distinct ways.
Apart from the word CALIFORNIA, 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.
