Question

a lock has a 4-digit code. each digit can be any number from 0-9. how many different codes are possible if digits can be repeated?

number of codes = ?

Explanation:

Identify the number of choices per digit

$$ \text{Digits available: } \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\} \implies 10 \text{ choices} $$

Apply the Fundamental Counting Principle

$$ \text{Total codes} = 10 \times 10 \times 10 \times 10 = 10^4 $$

Calculate the final value

$$ 10^4 = 10000 $$

Answer:

A lock has a 4-digit code. Each digit can be any number from 0-9. How many different codes are possible if digits can be repeated?

Number of Codes = <blank>10000</blank>