Final answer:
There are 60 possible three-letter words that can be made from the letters of the word "GUARD" without repeating any letters, calculated by multiplying the number of choices for each letter position: 5 x 4 x 3.
Step-by-step explanation:
The question asks how many three-letter words can be made from the letters of the word "GUARD" without repeating any letters. To solve this, we use combinatorics, which is a branch of mathematics dealing with combinations.
There are 5 letters in the word GUARD. The number of ways to make three-letter words is the number of ways to choose the first letter, multiplied by the number of ways to choose the second letter (after choosing the first), and then multiplied by the number of ways to choose the third letter (after choosing the first two).
For the first letter, we have 5 choices (G, U, A, R, D). After choosing the first letter, 4 letters remain for the second letter. So, there are 4 choices for the second letter. After choosing the first two letters, 3 letters remain for the third letter. Therefore, there are 3 choices for the third letter.
The number of different three-letter words that can be made from the letters of "GUARD" is therefore 5 × 4 × 3 = 60 possible combinations.