How Many Ways are There to Order the Letters of Word STANFORD?
The 8 letters word STANFORD can be arranged in 40320 distinct ways. The below detailed information shows how to find how many ways are there to order the letters STANFORD and how it is being calculated in the real world problems.
Distinguishable Ways to Arrange the Word STANFORD
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 STANFORD be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word STANFORD.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters STANFORD.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in STANFORD:
n = 8
Distinct subsets:
Subsets : S = 1; T = 1; A = 1; N = 1; F = 1; O = 1; R = 1; D = 1;
Subsets' count:
n1(S) = 1, n2(T) = 1, n3(A) = 1, n4(N) = 1, n5(F) = 1, n6(O) = 1, n7(R) = 1, n8(D) = 1
step 2 Apply the values extracted from the word STANFORD in the (nPr) permutations equation
nPr = 8!/(1! 1! 1! 1! 1! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8/{(1) (1) (1) (1) (1) (1) (1) (1)}
= 40320/1
= 40320
nPr of word STANFORD = 40320
Hence,
The letters of the word STANFORD can be arranged in 40320 distinct ways.
Apart from the word STANFORD, 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.
