If a lock requires 3 digits, how many different combinations can be formed using

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Question: If a lock requires 3 digits, how many different combinations can be formed using the digits 0-9?

Options:

Correct Answer: 1000

Solution:

Each digit can be any of the 10 digits, so the total combinations are 10^3 = 1000.

If a lock requires 3 digits, how many different combinations can be formed using the digits 0-9?

If a lock requires 3 digits, how many different combinations can be formed using the digits 0-9?

Step 1: Understand that a lock requires 3 digits.
Step 2: Know that the digits can be any number from 0 to 9.
Step 3: Realize that there are 10 possible choices for each digit (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
Step 4: Since there are 3 digits, and each digit can be chosen independently, you multiply the number of choices for each digit.
Step 5: Calculate the total combinations: 10 choices for the first digit, 10 choices for the second digit, and 10 choices for the third digit.
Step 6: This gives you 10 x 10 x 10, which is the same as 10^3.
Step 7: Calculate 10^3 to find the total number of combinations, which equals 1000.

Combinatorial Counting – Understanding how to calculate the total number of combinations by considering the number of choices for each position.