Unit 1 Permutations and Organized Counting

1.1 Organized Counting

p. 224#1-7 talk about them at your table.

Ex 1 Suppose that A, B, and C are three towns. There are three roads connecting A and B, and two roads connecting B and C. How many ways are there to get from A to C?

• Fundamental Counting Principle – if a task or process is made up of stages with separate choices, the total number of choices is where m is the number of choices in the first stage, n is the number of choices in the second stage, etc.

Ex 2 At a private school, students must wear school uniforms. Each student must wear a white, blue or grey shirt, black, grey, navy or white pants, black or brown shoes, and black, navy, white, grey or light blue socks. How many choices of uniform are possible?

Ex 3 How many ways are there to draw a red face card or a black ace from a standard deck?

• Additive Counting Principle – if one mutually exclusive action can occur in m ways, a second in n ways, etc, then there are ways in which one of these actions can occur.

• The key here is the use of AND or OR. If your multi-stage process requires the use of AND, you multiply the number of choices at each stage to get your total number. If your multi-stage process requires the use of OR, then you add the number of choices at each stage to get your total number.

Ex 4 Sailing ships used to send messages with signal flags flown from their masts. How many different signals are possible with a set of four distinct flags if a minimum of two flags is used for each signal?

Ex 5 A triathelete has four pairs of shoes in their bag. In how many ways can the triathelete pull out two unmatched shoes one after the other?

• Indirect Method – figure out the total number of ways of calculating the possibilities without restriction, then subtract the number of ways that don’t fit your problem-whatever is left, must be what you’re looking for.

p. 229#2-5, 8-9, 11-12, 15-16, 19-20