How many different 4-digit PINs can be formed using the digits 0-9 without repet

How many different 4-digit PINs can be formed using the digits 0-9 without repetition?

How many different 4-digit PINs can be formed using the digits 0-9 without repetition?

Step 1: Understand that a 4-digit PIN consists of 4 digits chosen from the digits 0 to 9.
Step 2: Realize that there are 10 possible digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
Step 3: Since we cannot repeat any digits in the PIN, we need to choose 4 different digits.
Step 4: For the first digit, we have 10 options (any digit from 0 to 9).
Step 5: For the second digit, we have 9 options left (since one digit has already been used).
Step 6: For the third digit, we have 8 options left (two digits have already been used).
Step 7: For the fourth digit, we have 7 options left (three digits have already been used).
Step 8: To find the total number of different 4-digit PINs, multiply the number of options for each digit: 10 * 9 * 8 * 7.
Step 9: Calculate the result: 10 * 9 = 90, then 90 * 8 = 720, and finally 720 * 7 = 5040.
Step 10: Conclude that the total number of different 4-digit PINs is 5040.

Permutations – The question tests the understanding of permutations, specifically how to calculate the number of ways to arrange a subset of items (digits) from a larger set without repetition.
Combinatorial Counting – It assesses the ability to apply combinatorial counting principles to determine the total number of unique arrangements of digits.