Question

Suppose an ATM PIN must consist of 6 numbers from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, with repeats allowed. For example, an acceptable PIN could be 955123. How many possible ATM PINs are possible?

Answer 1

There are one million possible ATM PINs, calculated as 10 to the power of 6 because there are 10 possible digits for each of the 6 positions in the PIN, allowing repetition.

Step-by-step explanation:

If an ATM PIN consists of 6 numbers, where each of the numbers can be any digit from 0 to 9, then for each position in the PIN, there are 10 possible choices. Since the digits can be repeated, each of the 6 positions can be filled independently from the others.

To find the total number of possible ATM PINs, we multiply the number of choices for each digit. This is because the number of possible outcomes of any repeated independent situation is the number of possibilities for one iteration raised to the power of the repetitions.

Therefore, the calculation for the total number of PINs is 10 (the number of choices for each digit) raised to the power of 6 (the number of digits in the PIN), which is 106. Calculating 106 gives us 1,000,000. Thus, there are one million possible combinations for a 6-digit ATM PIN where repeats are allowed.