Unique Ways to Arrange Alphabets of Word MARYLAND
The 8 letters word MARYLAND can be arranged in 20160 distinct ways. The below detailed information shows how to find how many ways are there to order the letters MARYLAND and how it is being arranged in the real world problems.
Unique Ways to Arrange the Word MARYLAND
The below step by step work generated by this permutation calculator shows how to find how many different ways, the letters of the word MARYLAND can be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word MARYLAND.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters MARYLAND.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in MARYLAND:
n = 8
Distinct subsets:
Subsets : M = 1; A = 2; R = 1; Y = 1; L = 1; N = 1; D = 1;
Subsets' count:
n1(M) = 1, n2(A) = 2, n3(R) = 1, n4(Y) = 1, n5(L) = 1, n6(N) = 1, n7(D) = 1
step 2 Apply the values extracted from the word MARYLAND in the (nPr) permutations equation
nPr = 8!/(1! 2! 1! 1! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8/{(1) (1 x 2) (1) (1) (1) (1) (1)}
= 40320/2
= 20160
nPr of word MARYLAND = 20160
Hence,
The letters of the word MARYLAND can be arranged in 20160 distinct ways.
Apart from the word MARYLAND, 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.
