Unique Ways to Arrange Alphabets 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 arranged in the real world problems.
Possible Arrangements of Alphabets in "HARVARD"
The 7 letters word HARVARD can be arranged in 1260 unique ways. Below is the list of all possible unique arrangements:
Unique Ways to Arrange the Word HARVARD
The below step by step work generated by this permutation calculator shows how to find how many different ways, the letters of the word HARVARD can 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.
