Question

Using the Fundamental Counting Principle, how many different ways can you select a 4-digit PIN for the lock, where the first and the last number cannot be zero, and repetitions are allowed?

A) 9,000
B) 9,720
C) 81,000
D) 90,000

Answer 1

The Fundamental Counting Principle is used to determine the number of different ways to select a 4-digit PIN for a lock, where the first and last number cannot be zero and repetitions are allowed. The answer is C) 81,000.

Step-by-step explanation:

The Fundamental Counting Principle is used to determine the number of different ways to select items from multiple sets. In this case, we are selecting a 4-digit PIN for a lock, where the first and last number cannot be zero and repetitions are allowed.

There are 9 possible choices for the first and last digit (1-9), and 10 possible choices for the second and third digit (0-9). Since repetitions are allowed, we multiply the number of choices for each digit together: 9 * 10 * 10 * 9 = 8,100.

Therefore, the answer is C) 81,000.