You write each of the 26 letters of the alphabet on separate index cards. If you choose 3 cards at random without replacing them, what is the probability of choosing A, B, and C?

1/15600

Step-by-step explanation:

This is a great example of what people call the Multiplication Principle.

First, find out how many ways the cards can be chosen.  You're picking 3 cards from a set of 26 without replacement.  The number of choices for the first card is 26, for the second card 25, for the third card 24.  The cards can be chosen in 26 x 25 x 24 = 15600 ways.

Now for the specific choice "A B C" the number of ways that can happen is

1 x 1 x 1  (one choice for the first card, 1 for the 2nd, 1 for the 3rd)

The probability is 1/15600