Finite – Retake Review – Chapter 6
Label the Venn diagram and answer questions.
1.) There were 250 people in the music store. 110 of them loved country , 67 of them loved rock, 22 of them loved both.
a.) n(people who loved neither country nor rock) =
b.) n(people who loved country and rock) =
c.) n(people who loved country or rock) =
2.) Shade the following.
a.) (A ∩ B’) b.) (A ∪ B)’ ∩ A c.) (A ∪ C)’ ∪ B
3.) A = {1,3,5,7,9,11} B = {1,2,3,4,5,6,7} U = {integers from 1 to 15}
Find:
a.) n(A)
b.) n(B')
c.) n(A ∩ B)
d.) n(A ∪ B)
e.) n(A ∩ B)'
f.) n(B)
4.) A and B are subsets of a universe U, where n(U) = 41, n(B) = 19, n(A’) = 26, and
n(A ∪ B)’ = 14. Find:
a.) n(A) = b.)n(A∩ B) =
Label the Venn diagram and answer the questions below.
5.) 38 people bought candy at the store. 16 bought
Twizzlers, 15 bought MilkDuds, and 19 bought Nerds.
5 bought MilkDuds and Twizzlers, 7 bought MilkDuds
and Nerds, 6 bought Twizzlers and Nerds, 3 bought all three.
a.) How many bought Twizzlers and Nerds but not MilkDuds? b.) How many bought Twizzlers not Nerds? c.) How many bought Nerds but not Twizzlers or Milkduds? d.) How many bought none of the three candies? e.) How many bought Twizzlers and Nerds? f.) How many bought Twizzlers or Nerds?
Set up and solve each problem below. SHOW ALL YOUR WORK.
6.) A home owner’s association is to elect a chairman and a secretary. There are four
candidates for chairman and five candidates for secretary. In how many different can
the officers be slated?
7.) I have 3 skirts, 3 blouses, and 2 pair of shoes.
a.) How many different outfits could be formed?
b.) Show the different options using a tree diagram.
8.) A quiz consists of six multiple choice questions with four possible responses to each question. In how many different ways can the quiz be answered?
9.) Joanie goes to the food court to get a salad and sandwich for lunch. The Daily Deli has 3 varieties of sandwiches and 2 salads. Better Bites has 4 varieties of sandwiches and 5 salads. The Lunch Spot has 6 varieties of sandwiches and 4 salads. Determine the number of ways she can select a sandwich and salad.
10) a.) Evaluate P(4, 3) b.) Evaluate C(6,2)
11.) In how many ways can the letters of the word REARRANGE be permuted?
12.) How many different words are possible using all the letters of the letters of PHANTOM?
13.) If a universal set contains 500 elements, n(A) = 240, n(A or B) = 460, n(A & B) = 55.
Find n(B’).
14.) The Boxing Committee asks that 2 members from each boxing club attend the next
committee meeting. The two students will be selected from one of the following
clubs: Joe’s with 22 members, Bob’s with 19 members, Tony’s with 25 members, and Tanya’s with 14 members. In how many ways can the 2 students be selected?
15.) A committee of 6 people is selected from a group of 7men and 8 women. In how many ways can the committee be selected so it contains at least one woman?
16.) The combination of a lock consists of four single digit numbers. How many possible combinations are there if:
a.) repetition of a number is allowed?
b.) no repetition of a number is allowed?
c.) the first digit must be a 1 with repetition?
d.) the first digit must be a 1 with no repetition?
17.) A club has 10 freshmen, 15 sophomores, 22 juniors, and 12 seniors. The executive group consists of a president, vice-president and a secretary which must be made up from only seniors, and a three member committee made up of only juniors. How many different ways can the board be formed?
18.) How many ways can 6 books be arranged on a shelf?
19.) A team of six people is selected at random from a group of 10 men and 8 women. Find the number of teams that contain at most 5 women.
20.) The Math Club has 12 juniors and 16 senior members. They need a President, Vice President, and Secretary that are seniors and four juniors to be on the publicity committee. How many ways can the five officers be chosen to fulfill the assignments?
21.) Let A = {6, 10, 15, 21, 30}, B = {6, 12, 24, 48}, C = {x l x is an integer divisible by 3}
Identify the following as true or false.
a. _____ b. _____
c. _____ d. _____
e. _____ f. _____
g. _____ h. _____
i. _____ j. A and B are ______