This document discusses counting and combinatorics. It introduces fundamental counting principles like the multiplication principle and factorial notation. It provides examples of counting problems like determining the number of ways coins can land on a table in a tree diagram, counting outfits from different numbers of pants and shirts, and seating arrangements of students in vacant seats. Factorial notation is defined as n! = n x (n-1) x (n-2) x ... x 3 x 2 x 1, with examples provided to calculate factorials.

1. Counting
A.K.A.
Combinatorics
Heeley City Farm 014_edited-1 hopscotch by flickr user incurable_hippie

2. In how many ways can 5 people be seated in a straight line?

3. A nickel and a quarter and a dime are tossed on a table. Create a
tree diagram to determine how many ways these coins can land
on the table. (The order in which the coins land doesn't matter; it
will next week.)

4. The Fundamental Principle of Counting
If there are M ways to do a first thing and N ways to do a second
thing, then there are M x N ways to do both things.
Example: How many outfits can be made from 3 pants and 4 shirts?

5. In how many ways can six students be seated in 8 vacant seats?