If a lock has 4 digits, how many different combinations can be formed if digits

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Question: If a lock has 4 digits, how many different combinations can be formed if digits can be repeated?

Options:

Correct Answer: 10000

Solution:

Each digit can be any of the 10 digits (0-9). Therefore, the total combinations = 10^4 = 10000.

If a lock has 4 digits, how many different combinations can be formed if digits can be repeated?

If a lock has 4 digits, how many different combinations can be formed if digits can be repeated?

Step 1: Understand that a lock with 4 digits means there are 4 positions to fill with digits.
Step 2: Recognize that each position can be filled with any digit from 0 to 9.
Step 3: Count the total number of digits available, which is 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).
Step 4: Since digits can be repeated, each of the 4 positions can independently be any of the 10 digits.
Step 5: Calculate the total combinations by multiplying the number of choices for each position: 10 (for the first digit) * 10 (for the second digit) * 10 (for the third digit) * 10 (for the fourth digit).
Step 6: This can be simplified using exponents: 10^4.
Step 7: Calculate 10^4, which equals 10000.
Step 8: Conclude that there are 10000 different combinations possible for the lock.

Combinatorics – The question tests the understanding of counting principles, specifically the multiplication principle where each digit can be chosen independently.
Permutations with Repetition – It assesses the ability to calculate combinations when repetition of elements (digits) is allowed.