Precalculus
Name_______________________________
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Sections 9.1 and 9.3
For problems 1-6 you must show the set up for the problem as well as the final answer.
1. There are 10 students in a class that meets in a room that has 12 chairs arranged in a row.
How many ways is it possible for the students to be seated?
2. A golf club manufacturer makes irons with 7 different shaft lengths, 3 different grips, and 2
different club head materials. How many different types of irons are possible?
3. How many 7-digit telephone numbers can be formed if the first digit cannot be 0 or 1?
(repetition is allowed).
4. To win the Powerball lottery, you must correctly choose five numbers between1 and 59 (the
numbers can not repeat and order does not matter) and the powerball which is one number
between 1 and 35. How many ways can you choose a Powerball ticket? (Hint: Do each part
separately, then multiply your answers.)
5. In the 2014 Winter Olympics 32 men competed in the Ski Slopestyle event. How many ways
could the Gold, Silver and Bronze medals have been awarded?
6. You are planning to take a Mediterranean cruise. One day you have four choices of restaurants
for lunch (choose one), five choices of restaurants for dinner (choose one) and up to 8 different
activities to choose from. You know you will pick at least one activity. How many choices do
you have when planning your day?
7. 9 quarters with dates from 2001 to 2009 are tossed. (Use binomial distribution)
a. What is the probability that only coins 2002 and 2005 land heads up?
b. What is the probability that at least 3 coins land tails up?
8. A fair six-sided die is tossed 8 times.
a. What is the probability of rolling a 6 five times?
b. What is the probability of rolling a 6 at least two times?
9. A group of people were surveyed about where they like to go on vacation. 63% like to go to
the beach. 22% like to go to mountain resorts. Of those that stated they like to go to the beach
18% of them also like to go to mountain resorts.
a. Construct a Venn diagram correctly displaying all of the information. Make sure all regions
are labeled and assigned a numerical probability. Round to four decimal places.
b. If a person is chosen at random, what is the probability they do not like to go to the beach or
mountain resorts?
9. There are two jars of candy, one is blue and the other is red. In the blue candy jar there is 10
M&M’s, 8 Skittles, and 7 Reese’s Pieces. The red candy jar has 7 M&M’s, 5 Skittles, and 8 Reese’s
Pieces. Construct a tree diagram and answer the following questions. (Round to three decimal
places).
a. You have picked a Skittle, what is the probability it came from the blue candy jar?
b. You have picked a Reese’s Piece, what is the probability it came from the red candy jar?