Question

To use an automated teller machine at a certain​ bank, you must enter a 4​-digit ​code, using the digits 0 dash 9. How many 4​-digit codes are possible if repetition of digits is​ permitted?

Answer 1

The number of possible 4-digit codes with repetition allowed using the digits 0-9 is
`10^4`, which equals 10,000 since each position can be filled by any of the ten digits independently.

Step-by-step explanation:

To determine the number of possible 4-digit codes with repetition allowed using the digits 0-9, one needs to consider that each digit in the code can be any of the ten digits. For each position in the 4-digit code, there are 10 options. Since there are 4 positions, and the choices are independent of each other, the number of different combinations can be found by multiplying the number of options for each position.

The calculation would be: 10 × 10 × 10 × 10 because there are 10 choices for the first digit, 10 choices for the second digit, 10 choices for the third digit, and 10 choices for the fourth digit.

Step-by-Step Calculation

First digit: 10 possibilities

Second digit: 10 possibilities

Third digit: 10 possibilities

Fourth digit: 10 possibilities

Therefore, the total number of possible 4-digit codes is
`10^4`, which is 10,000.1