Question

In how many different ways can the letters of the word MUSIC be arranged?

• A. 100
• B. 110
• C. 120
• D. 142

Hint:

If a word has repeated letters, the formula is slightly different. You divide n! by the factorial of the count of each repeated letter. For example, for the word "APPLE" (5 letters, 'P' is repeated twice), the number of arrangements would be \( \frac{5!}{2!} = \frac{120}{2} = 60 \).

Answer 1

The Correct Option is C

Step 1: Understanding the Problem
The problem asks for the number of different arrangements (permutations) of the letters in the word "MUSIC".

Step 2: Key Formula or Approach
The number of ways to arrange 'n' distinct objects is given by n! (n factorial), where \( n! = n \times (n-1) \times (n-2) \times ... \times 1 \).

Step 3: Detailed Explanation
1. Count the letters and check for repetition:
The word "MUSIC" has 5 letters: M, U, S, I, C.
All the letters are distinct (no letter is repeated).
2. Apply the permutation formula:
Since we are arranging 5 distinct letters, the number of possible arrangements is 5!.
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 \] \[ 5! = 20 \times 6 \] \[ 5! = 120 \] So, the letters of the word "MUSIC" can be arranged in 120 different ways.

Step 4: Final Answer
The number of different arrangements is 120. Therefore, option (C) is the correct answer.