Unique Ways to Arrange Alphabets of Word FRACTIONS
The 9 letters word FRACTIONS can be arranged in 362880 distinct ways. The below detailed information shows how to find how many ways are there to order the letters FRACTIONS and how it is being arranged in the real world problems.
Unique Ways to Arrange the Word FRACTIONS
The below step by step work generated by this permutation calculator shows how to find how many different ways, the letters of the word FRACTIONS can be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word FRACTIONS.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters FRACTIONS.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in FRACTIONS:
n = 9
Distinct subsets:
Subsets : F = 1; R = 1; A = 1; C = 1; T = 1; I = 1; O = 1; N = 1; S = 1;
Subsets' count:
n1(F) = 1, n2(R) = 1, n3(A) = 1, n4(C) = 1, n5(T) = 1, n6(I) = 1, n7(O) = 1, n8(N) = 1, n9(S) = 1
step 2 Apply the values extracted from the word FRACTIONS in the (nPr) permutations equation
nPr = 9!/(1! 1! 1! 1! 1! 1! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9/{(1) (1) (1) (1) (1) (1) (1) (1) (1)}
= 362880/1
= 362880
nPr of word FRACTIONS = 362880
Hence,
The letters of the word FRACTIONS can be arranged in 362880 distinct ways.
Apart from the word FRACTIONS, 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.
