Question 2.68

38.

  1. A credit-card company makes it easier for customers to memorize their PIN (personal identification number) by using a four-digit PIN that consists of three different digits selected from 0, 1, 2,… 9, where one of the digits must be a zero, another is a nonzero digit that is repeated, and another is a digit different from these two. How many different PINs of this kind are there?
  2. How many PINs are possible if there are no restrictions on repeats of the 10 possible digits that can be used?