Final answer:
The possible values of X, the number of nonzero digits in a randomly selected 4-digit PIN with no restrictions, are 1, 2, 3, and 4. For example, a PIN like 2047 would have X = 3, as there are three nonzero digits.
Step-by-step explanation:
When selecting a 4-digit PIN, each digit can be any number from 0 to 9. To determine the possible values of X, we consider the number of nonzero digits in the PIN. Let's explore three examples:
1. PIN = 0123: In this case, X = 3, as there are three nonzero digits (1, 2, and 3).
2. PIN = 5670: Here, X = 3, as there are three nonzero digits (5, 6, and 7).
3. PIN = 8888: In this example, X = 0, as there are no nonzero digits.
The possible values of X range from 0 to 4, depending on how many nonzero digits are present in the PIN. It's important to note that X cannot exceed 4, as we are dealing with 4-digit PINs. Understanding the possible values of X is essential in analyzing the distribution of PIN combinations and their characteristics.