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

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

Options:

Correct Answer: 24

Solution:

The number of arrangements of 4 letters is 4! = 4 × 3 × 2 × 1 = 24.

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

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

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 different arrangements of 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 every whole number less than it down to 1.
Step 4: Perform the multiplication: 4 × 3 × 2 × 1.
Step 5: Calculate the result: 4 × 3 = 12, then 12 × 2 = 24, and finally 24 × 1 = 24.
Step 6: Conclude that there are 24 different ways to arrange the letters in the word 'MATH'.

Permutations – The arrangement of a set of items in a specific order, calculated using factorial notation.