Counting and Listing Problems

1. (Multiplication Principle)
  1. Suppose you flip a coin and roll a die, list all the possible outcomes below. (I started the list for you. H1 stands for getting a head on the coin and rolling a 1 on the die.)
  2. How many possible outcomes are there?

2. (Permutation)
  1. Dick, Jane, Sally, and Spot are marching in a line. List all the possible ways they can line up? (Again, I have started it for you. I used P for Spot.)
  2. How many possible outcomes are there?
3. (Simple Combination)
  1. Suppose Samantha is going on a trip with her family and she gets to choose 3 toys to take with her out of the following: Ball, Elmo, Fishie, Popper, Teddie Bear. List all the ways she could choose three toys.

  2. Is choosing Elmo then the ball a different outcome than choosing the ball then Elmo?

  3. How many different outcomes are there?

4. (Addition Principle)
Suppose our class is going to enter a 4 person relay team and there must be at least one person of each gender on the team. There are 13 males and 12 females in the class.
  1. How many ways can we enter a team with one female and three males?

  2. How many ways can we enter a team with two females and two males?

  3. How many ways can we enter a team with three females and one male?

  4. How many ways can we enter a team?

5. (Binomial Theorem)
Suppose Fred has four recipes that he is considering entering into a cooking contest. The contest allows you to enter as many as you want, but when Fred cooks sometimes things don’t come out right. He only wants to enter the recipes that came out perfectly today. List the number of ways he could enter the contest. Use A, B, C, D to represent his four recipes.


Solutions