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How many ways can you arrange the letters in the word 'MATH'?

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Question: How many ways can you arrange the letters in the word \'MATH\'?

Options:

  1. 12
  2. 24
  3. 16
  4. 20

Correct Answer: 24

Solution: 

The number of arrangements = 4! = 24.

How many ways can you arrange the letters in the word 'MATH'?

Practice Questions

Q1
How many ways can you arrange the letters in the word 'MATH'?
  1. 12
  2. 24
  3. 16
  4. 20

Questions & Step-by-Step Solutions

How many ways can you arrange the letters in the word 'MATH'?
Correct Answer: 24
  • Step 1: Identify the number of letters in the word 'MATH'. There are 4 letters: M, A, T, H.
  • Step 2: Understand that to find the number of ways to arrange these letters, we use the factorial of the number of letters.
  • Step 3: Calculate the factorial of 4, which is written as 4!. This means you multiply 4 by all the whole numbers less than it: 4 x 3 x 2 x 1.
  • Step 4: Perform the multiplication: 4 x 3 = 12, then 12 x 2 = 24, and finally 24 x 1 = 24.
  • Step 5: Conclude that there are 24 different ways to arrange the letters in the word 'MATH'.
  • Permutations – The question tests the understanding of permutations, specifically how to calculate the number of ways to arrange distinct items.
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