If a lock requires a 3-digit code using the digits 0-9, how many different codes
Practice Questions
Q1
If a lock requires a 3-digit code using the digits 0-9, how many different codes can be formed if digits cannot be repeated?
720
1000
900
800
Questions & Step-by-Step Solutions
If a lock requires a 3-digit code using the digits 0-9, how many different codes can be formed if digits cannot be repeated?
Step 1: Understand that we need to create a 3-digit code using the digits from 0 to 9.
Step 2: Realize that there are 10 different digits available (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
Step 3: For the first digit of the code, you can choose any of the 10 digits. So, there are 10 options.
Step 4: For the second digit, you cannot use the digit you already chose for the first digit. This leaves you with 9 options.
Step 5: For the third digit, you cannot use the first or second digit. This leaves you with 8 options.
Step 6: To find the total number of different codes, multiply the number of options for each digit together: 10 (first digit) * 9 (second digit) * 8 (third digit).
Step 7: Calculate the total: 10 * 9 * 8 = 720.
Permutations – The question tests the understanding of permutations where the order matters and digits cannot be repeated.
Counting Principles – It assesses the ability to apply the fundamental counting principle to determine the total number of combinations.
