Homework 18

Details

1. A department assigns identification codes to students. Each code is created in one of the following ways:
   • Type 1: Three uppercase letters followed by two digits.
   • Type 2: Five digits.

   There are 26 letters, 10 digits, and both letters and digits may be repeated. Briefly justify your answer to each of the following questions.

   1. (3) How many codes of Type 1 are possible?
   2. (3) How many codes of Type 2 are possible?
   3. (3) How many distinct codes are possible in total?
   4. (3) What is the minimum number of students that guarantees that at least two students must receive the same identification code? Prove your answer.