1: Combinatorics

Foreshadowing: Combinatorics

This module will make heavy use of the ‘Law of Combining’, which you probably learned in grade school,
but without the fancy name. For example, in grade school you got a problem something like this:

Nancy Drew, girl detective, is heading out to Solve the Case. She has 3 blouses and 4 skirts in her closet
(the housekeeper is behind on the laundry). How many different outfits can Nancy make?

Here is one way to visualise Nancy ‘s outfits:

Here is another way (called a tree diagram):

Either way, you have to agree that Nancy has 12 possible outfits (although her father, famous lawyer
Carson Drew, will probably veto the tank-top/miniskirt combination).

You will probably also have noticed that 12 = 3 x  4  is not a coincidence. There are 3 kinds of
tops Nancy could put on, and for each of these, she could choose 4 skirts.

The Law of Combining says:

If you want to count the possible combinations of ONE item from set 1 and ONE item from
set 2, you can just multiply the number of elements in set 1 by the number of elements  set 2.

Or simply,

N_tot = N₁ x N₂

Just pull out your trusty calculator.
No calculator? Go to Google, type in the equation (i.e., “17 x 32=”) and hit enter!