How many different 4-digit PIN codes can be formed using the digits 0-9 if repetition is allowed?
Practice Questions
1 question
Q1
How many different 4-digit PIN codes can be formed using the digits 0-9 if repetition is allowed?
10000
1000
5000
9000
The number of 4-digit PIN codes is 10^4 = 10000.
Questions & Step-by-step Solutions
1 item
Q
Q: How many different 4-digit PIN codes can be formed using the digits 0-9 if repetition is allowed?
Solution: The number of 4-digit PIN codes is 10^4 = 10000.
Steps: 6
Step 1: Understand that a 4-digit PIN code consists of 4 positions, and each position can be filled with any digit from 0 to 9.
Step 2: Realize that there are 10 possible digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) for each position.
Step 3: Since repetition of digits is allowed, the choice for each of the 4 positions is independent of the others.
Step 4: Calculate the total number of combinations by multiplying the number of choices for each position: 10 choices for the first position, 10 for the second, 10 for the third, and 10 for the fourth.
Step 5: This can be expressed mathematically as 10 * 10 * 10 * 10, which is the same as 10^4.
Step 6: Calculate 10^4, which equals 10000. Therefore, there are 10000 different 4-digit PIN codes.
