Question

How many different 3-letter words can be formed from the letters of the word “MATH” without repetition?

• A. 12
• B. 18
• C. 24
• D. 36

Hint:

"Without repetition" means every time you pick a letter, your options for the next spot decrease by one. If repetition was allowed, the answer would be $4 \times 4 \times 4 = 64$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem involves permutations because the order of letters matters when forming "words." We are choosing $r=3$ items from a total set of $n=4$ unique items (M, A, T, H).

Step 2: Key Formula or Approach:
The number of permutations of $n$ things taken $r$ at a time is given by: \[ P(n, r) = \frac{n!}{(n-r)!} \] Alternatively, we can use the "Box Method": - 1st position: 4 choices - 2nd position: 3 choices (since repetition is not allowed) - 3rd position: 2 choices

Step 3: Calculation:
Using the Multiplication Principle: \[ \text{Total Words} = 4 \times 3 \times 2 = 24 \]

Step 4: Final Answer:
There are 24 different 3-letter words that can be formed.