How many different 4-digit PIN codes can be formed using the digits 0-9 if repet

How many different 4-digit PIN codes can be formed using the digits 0-9 if repetition is allowed?

How many different 4-digit PIN codes can be formed using the digits 0-9 if repetition is allowed?

Correct Answer: 10000

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.

Combinatorics – The problem involves calculating the total number of combinations of digits for a 4-digit PIN code, considering that each digit can be any of the 10 digits (0-9) and that repetition is allowed.
Permutations with Repetition – The calculation uses the principle of permutations with repetition, where the number of choices for each digit remains constant across all positions.