How many permutations are possible with the letters "ABC"?

How many permutations are possible with the letters "ABC"?

• A. 3
• B. 4
• C. 5
• D. 6

Answer: (D)

To determine the number of permutations possible with the letters "ABC," one needs to arrange all the letters in different sequences. Permutations refer to the different ways to order elements, taking into account the sequence of arrangement. For three distinct letters, the total number of permutations can be calculated using the factorial of the number of items being arranged. In this case, since there are 3 letters (A, B, C), the formula used is factorial of 3, represented as 3! (3 factorial). Calculating this: 3! = 3 × 2 × 1 = 6. This means there are 6 unique arrangements or permutations of the letters. The actual permutations are ABC, ACB, BAC, BCA, CAB, and CBA. Each arrangement is distinct, reinforcing the fact that there are indeed 6 unique ways to arrange the letters "ABC." The other options do not reflect the correct number of arrangements for three unique letters, as they either undercount or miscount the possibilities. Understanding and applying the factorial function for counting permutations is essential in solving such problems.

To determine the number of permutations possible with the letters "ABC," one needs to arrange all the letters in different sequences. Permutations refer to the different ways to order elements, taking into account the sequence of arrangement.

For three distinct letters, the total number of permutations can be calculated using the factorial of the number of items being arranged. In this case, since there are 3 letters (A, B, C), the formula used is factorial of 3, represented as 3! (3 factorial).

Calculating this:

3! = 3 × 2 × 1 = 6.

This means there are 6 unique arrangements or permutations of the letters. The actual permutations are ABC, ACB, BAC, BCA, CAB, and CBA. Each arrangement is distinct, reinforcing the fact that there are indeed 6 unique ways to arrange the letters "ABC."

The other options do not reflect the correct number of arrangements for three unique letters, as they either undercount or miscount the possibilities. Understanding and applying the factorial function for counting permutations is essential in solving such problems.