How Many Ways are There to Order the Letters of Word AMERICA?
The 7 letters word AMERICA can be arranged in 2520 distinct ways. The below detailed information shows how to find how many ways are there to order the letters AMERICA and how it is being calculated in the real world problems.
Distinguishable Ways to Arrange the Word AMERICA
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 AMERICA be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word AMERICA.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters AMERICA.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in AMERICA:
n = 7
Distinct subsets:
Subsets : A = 2; M = 1; E = 1; R = 1; I = 1; C = 1;
Subsets' count:
n1(A) = 2, n2(M) = 1, n3(E) = 1, n4(R) = 1, n5(I) = 1, n6(C) = 1
step 2 Apply the values extracted from the word AMERICA in the (nPr) permutations equation
nPr = 7!/(2! 1! 1! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5 x 6 x 7/{(1 x 2) (1) (1) (1) (1) (1)}
= 5040/2
= 2520
nPr of word AMERICA = 2520
Hence,
The letters of the word AMERICA can be arranged in 2520 distinct ways.
Apart from the word AMERICA, 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.
