How many different 4-digit PINs can be formed using the digits 0-9 if digits cannot be repeated?
Practice Questions
1 question
Q1
How many different 4-digit PINs can be formed using the digits 0-9 if digits cannot be repeated?
5040
10000
9000
7200
The first digit can be any of 10 digits, the second can be any of 9, the third can be any of 8, and the fourth can be any of 7. Total = 10 * 9 * 8 * 7 = 5040.
Questions & Step-by-step Solutions
1 item
Q
Q: How many different 4-digit PINs can be formed using the digits 0-9 if digits cannot be repeated?
Solution: The first digit can be any of 10 digits, the second can be any of 9, the third can be any of 8, and the fourth can be any of 7. Total = 10 * 9 * 8 * 7 = 5040.
Steps: 7
Step 1: Understand that a 4-digit PIN consists of 4 positions, and each position can be filled with a digit from 0 to 9.
Step 2: For the first digit, you can choose any of the 10 digits (0-9). So, there are 10 options for the first digit.
Step 3: For the second digit, you cannot use the digit you chose for the first digit. This leaves you with 9 remaining options.
Step 4: For the third digit, you cannot use the first or second digit. This leaves you with 8 options.
Step 5: For the fourth digit, you cannot use the first, second, or third digit. This leaves you with 7 options.
Step 6: To find the total number of different 4-digit PINs, multiply the number of options for each digit together: 10 (first) * 9 (second) * 8 (third) * 7 (fourth).
