How Many Ways are There to Order the Letters of Word MATH?
The 4 letters word MATH can be arranged in 24 distinct ways. The below detailed information shows how to find how many ways are there to order the letters MATH and how it is being calculated in the real world problems.
Distinguishable Ways to Arrange the Word MATH
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 MATH be arranged.
Objective:
Find how many distinguishable ways are there to order the letters in the word MATH.
Step by step workout:
step 1 Address the formula, input parameters and values to find how many ways are there to order the letters MATH.
Formula:
nPr =n!/(n1! n2! . . . nr!)
Input parameters and values:
Total number of letters in MATH:
n = 4
Distinct subsets:
Subsets : M = 1; A = 1; T = 1; H = 1;
Subsets' count:
n1(M) = 1, n2(A) = 1, n3(T) = 1, n4(H) = 1
step 2 Apply the values extracted from the word MATH in the (nPr) permutations equation
nPr = 4!/(1! 1! 1! 1! )
= 1 x 2 x 3 x 4/{(1) (1) (1) (1)}
= 24/1
= 24
nPr of word MATH = 24
Hence,
The letters of the word MATH can be arranged in 24 distinct ways.
Apart from the word MATH, 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.
