How many different 4-digit PINs can be formed using the digits 0-9 if digits can

How many different 4-digit PINs can be formed using the digits 0-9 if digits cannot be repeated?

How many different 4-digit PINs can be formed using the digits 0-9 if digits cannot be repeated?

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).
Step 7: Calculate the total: 10 * 9 * 8 * 7 = 5040.

Permutations – The question tests the understanding of permutations where the order matters and repetition is not allowed.
Counting Principles – It assesses the ability to apply the fundamental counting principle to determine the total number of combinations.