Anthony J. answered • 08/26/20

Mr. J Math & Science Tutor (Prior Teacher)

For the first question,

We will start with the total number of 4 digit pins, then 5 digit pins, and 6 digit pins.

4 digit pins: 10 * 10 * 10 * 10 = 1000 (as each digit of the pin has no restrictions and can be 0 - 9)

5 digit pins: 10 * 10 * 10 * 10 * 10 = 10000 (as each digit of the pin has no restrictions and can be 0 - 9)

6 digit pins: 10 * 10 * 10 * 10 *10 * 10 = 10000 (as each digit of the pin has no restrictions and can be 0 - 9)

Due to how the digit pins can be 4, 5, or 6 digits in length we will add those combinations. 1000 + 10000 + 100000 = 111,000 different possible pin numbers based on no restriction pins of length 4, 5, or 6.