Question

Justin is choosing a 2-letter password from the letters A, B, and C. The password cannot have the same letter repeated in it. How many such passwords are possible?

Answer 1

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.