Question

Pigeonhole Principle:

1. What is the minimum number of students that must be assigned to a classroom with 14 tables to guarantee that some table will have at least 3 students?

2. Suppose a set of 8 numbers are selected from the set {1, 2, 3, ..., 13, 14}. Show that two of the selected numbers must sum to 15. (Hint: think about how many subsets of 2 elements you can form such that the sum of the values of the two elements is 15)

Sum Rule and Product Rule

1. Henry owns 3 hiking socks and 5 running socks for his left foot. He owns 12 ankle socks for his right foot. How many different pairs of socks, one left and one right sock, can he form? Henry, the odd guy that he is, doesnt mind mixing a hiking or running sock with an ankle sock.

2. Regular MA license plates have 3 digits followed by 3 (uppercase) letters, e.g. 924 VXA or 4 digits followed by 2 (uppercase) letters, e.g. 2012 CS. How many different license plates are possible?

Answer 1