Lesson Review:

We introduced 4 basic counting techniques today:

1) Casework: to divide the problem into different subcases, count each, and add the counts altogether. It helps break a counting problem into manageable pieces, but requires you to be organized and careful (do not omit any outcomes).

2) Complementary Method: what we want = total = what we do not want. n(A) = n(U)-n(A’)

3) Constructive Method: count how many ways we can construct a particular item.

4) Counting with restrictions: it is generally best to deal with the most severe restrictions first.

Some tips:

1) independent choices: multiply the number of options at each step; exclusive options: add the number of options.

2) Sometimes when you get stuck at complicated problems, try to start with some simple cases, and find a pattern, or hint, to help you solve the “big problem”.

Homework:

Page 34: Ex2.2.1, 2.2.3, 2.2.5* (*bonus, highly recommended)
Page 38: Ex 2.3.1, 2.3.3
Page 41: Ex 2.4.1, 2.4.3
Page 44: Ex 2.5.1, 2.5.4