Final answer:
There are 3 possible 2-letter passwords that can be formed from the letters A, B, and C.
Step-by-step explanation:
To find the number of possible passwords, we need to determine the number of combinations that can be made by choosing 2 letters from the set of A, B, and C.
We can solve this problem using the concept of permutations. In a permutation, the order of the elements matters. In this case, we need to choose 2 letters without repetition, so we can use the formula for the number of permutations of 3 objects taken 2 at a time.
The formula for the number of permutations is nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects chosen at a time.
Using this formula, we can calculate the number of combinations:
3P2 = 3! / (3-2)! = 3! / 1! = 3
Therefore, there are 3 possible 2-letter passwords that can be formed from the letters A, B, and C.