How many 4-digit personal identification numbers are possible if the number cannot contain a zero?
A. 5,040
B. 6,561
C. 9,000
D. 10,000
Answer (1)
Each of the 4 digits in the PIN can be any of the 9 digits (1-9).
The total number of possible PINs is calculated by multiplying the number of choices for each digit: 9 × 9 × 9 × 9 .
This simplifies to 9 4 .
Therefore, the total number of possible PINs is 6561 .
Explanation
Understand the problem We need to determine the number of 4-digit PINs possible where each digit can be any number from 1 to 9, excluding 0.
Determine the number of choices for each digit Since the PIN is 4 digits long, and each digit can be chosen from the numbers 1 through 9, there are 9 possible choices for each digit.
Calculate the total number of PINs To find the total number of possible PINs, we multiply the number of choices for each digit together. This is because each digit is chosen independently. So, the total number of PINs is 9 × 9 × 9 × 9 .
State the final answer Calculating this product, we get 9 4 = 6561 . Therefore, there are 6,561 possible 4-digit PINs that do not contain a zero.
Examples
In creating secure access codes, like for a bank card or online account, it's important to know how many different combinations are possible. If you decide that your 4-digit PIN cannot include the number 0, then you have 9 choices (1-9) for each digit. Knowing there are 6,561 possible PINs helps assess the security level and the likelihood of someone guessing the correct code.
