Question

Ethan forgot the five-digit code to the lock on his briefcase. However, he did remember that the first digit is 6 and the last digit is either 8 or 4. The middle digits could be any number from 0 through 9 inclusive. What is the greatest number of five-digit codes Ethan might have to try in order to to open his briefcase?

Answer 1

The 1st digit is known. (times 1) The last, (5th digit is of 2 choices (times 2). The middle 3 numbers are of 10 choices (0-9) (times 10 for each).

1 * 10 * 10 * 10 * 2 = 2,000 five-digit codes