ProbStat 4.1 worksheet #2

Brianna is painting the 4 rooms in her apartment. If she has 6 colors of paint to choose from, using one color in each room and she can use the same color in more than one room, how many ways can she paint the rooms?

Answer explanation

6 x 6 x 6 x 6 = 6^4

A skate shop is setting up a display with 5 different boards. How many ways can they arrange the boards?

Answer explanation

5! = 5 x 4 x 3 x 2 x 1

It’s Taco Tuesday! If you can choose one of 3 different shell types, one of 4 different meats, one of 3 cheeses, and either hot, medium, mild, or no sauce, how many ways can you make your taco?

Answer explanation

3 x 4 x 3 x 4

Andre is setting up his workout plan for the day. He has 3 warm up exercises to do first, then 5 weight exercises, then 1 cardio activity, followed by 2 cool down exercises, and lastly will do 10 different stretches. How many ways can he complete his workout? (HINT: he is doing ALL of each type of exercise before moving on to the next type of exercise)

Answer explanation

3! x 5! x 1 x 2! x 10!

How many outcomes are possible when rolling two dice and spinning the spinner shown?

Answer explanation

6 x 6 x 5

How many outcomes are possible when rolling two dice and spinning the spinner shown?

Answer explanation

6 x 6 x 4 (there are only 4 different colors)

You are creating a 6 element password for an online account. The password must contain only upper case letters, digits (0-9), and at least one of the special characters $, @, or * 

How many passwords are possible if all elements can be repeated?

Answer explanation

39 x 39 x 39 x 39 x 39 x 39 = 39^6

You are creating a 6 element password for an online account. The password must contain only upper case letters, digits (0-9), and at least one of the special characters $, @, or * 

How many passwords are possible if your first and last element cannot be a special character and repetitions are allowed?

Answer explanation

36 x 39 x 39 x 39 x 39 x 36

You are creating a 6 element password for an online account. The password must contain only upper case letters, digits (0-9), and at least one of the special characters $, @, or * 

How many passwords are possible if repetitions are NOT allowed?

Answer explanation

39 x 38 x 37 x 36 x 35 x 34

You are creating a 6 element password for an online account. The password must contain only upper case letters, digits (0-9), and at least one of the special characters $, @, or * 

How many passwords are possible if your first element must be a digit, your last element must be a letter, and repetitions are allowed?

Answer explanation

10 x 39 x 39 x 39 x 39 x 26