How Many Ways are There to Order the Letters of Word LAUGH?
The 5 letters word LAUGH can be arranged in 120 distinct ways. The below detailed information shows how to find how many ways are there to order the letters LAUGH and how it is being calculated in the real world problems.
Distinguishable Ways to Arrange the Word LAUGH
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 LAUGH be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word LAUGH.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters LAUGH.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in LAUGH:
n = 5
Distinct subsets:
Subsets : L = 1; A = 1; U = 1; G = 1; H = 1;
Subsets' count:
n1(L) = 1, n2(A) = 1, n3(U) = 1, n4(G) = 1, n5(H) = 1
step 2 Apply the values extracted from the word LAUGH in the (nPr) permutations equation
nPr = 5!/(1! 1! 1! 1! 1! )
= 1 x 2 x 3 x 4 x 5/{(1) (1) (1) (1) (1)}
= 120/1
= 120
nPr of word LAUGH = 120
Hence,
The letters of the word LAUGH can be arranged in 120 distinct ways.
Apart from the word LAUGH, 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.
