# How Many Ways are There to Order the Letters of Word HARVARD?

The 7 letters word HARVARD can be arranged in 1260 distinct ways. The below detailed information shows how to find how many ways are there to order the letters HARVARD and how it is being calculated in the real world problems.

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Distinguishable Ways to Arrange the Word HARVARD
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 HARVARD be arranged.

Objective:
Find how many distinguishable ways are there to order the letters in the word HARVARD.

Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters HARVARD.
Formula:
nPr =n!/(n1! n2! . . . nr!)

Input parameters and values:
Total number of letters in HARVARD:
n = 7

Distinct subsets:
Subsets : H = 1; A = 2; R = 2; V = 1; D = 1;
Subsets' count:
n1(H) = 1, n2(A) = 2, n3(R) = 2, n4(V) = 1, n5(D) = 1

step 2 Apply the values extracted from the word HARVARD in the (nPr) permutations equation
nPr = 7!/(1! 2! 2! 1! 1! )

= 1 x 2 x 3 x 4 x 5 x 6 x 7/{(1) (1 x 2) (1 x 2) (1) (1)}

= 5040/4

= 1260
nPr of word HARVARD = 1260

Hence,
The letters of the word HARVARD can be arranged in 1260 distinct ways.

Apart from the word HARVARD, 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. 