Round #1009

How many ways can you arrange the letters of the word "MATHS"?

## Step 1: Determine the total number of letters in the word "MATHS" The word "MATHS" has 5 letters. ## Step 2: Identify any repeated letters in the word "MATHS" There are no repeated letters in the word "MATHS", as each letter (M, A, T, H, S) appears only once. ## Step 3: Apply the formula for permutations of a set of distinct items The number of ways to arrange n distinct items is given by n!, where "!" denotes factorial, the product of all positive integers up to that number. For "MATHS", n = 5. ## Step 4: Calculate the factorial of 5 5! = 5 × 4 × 3 × 2 × 1 = 120. The final answer is: $\boxed{120}$

5! / (1! * 1! * 1! * 1! * 1!) = 120