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How many different outfits could be formed with two skirts and three blouses. Show the different options using a tree diagram.

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?

A quiz consists of four multiple choice questions with five possible responses to each question. In how many different ways can the quiz be answered?

Jamie goes to the food court to get a salad and sandwich for lunch. The Daily Deli has 5 varieties of sandwiches and 2 salads. Better Bites has 3 varieties of sandwiches and 6 salads. The Lunch Spot has 8 varieties of sandwiches and 5 salads. Determine the number of ways she can select a sandwich and salad.

In how many arrangements can 3 men and 3 women be seated in a row if no one sits next to a member of the same gender?

What is the symbol for element?

A = set of all positive even integers B = set of all positive multiples of 3 Describe and list the elements in the intersection of the two sets.

A = all multiples of 3 B = all multiples of 4 Are sets A & B disjoint?

List all of the elements of the set {x | (x + 2)(x – 5)(x – 7) = 0}

A is the set of students at Winfield College Who had a 4.0 GPA for the Fall Semester. B is the set of students at Winfield College Who had a 4.0 GPA for the Spring Semester. 1.Describe the union of A & B 2.Describe the intersection of A & B 3.Is A a subset of B?

A = {a, b, c, d, e, f} B = {a, e, i, o, u, y} Compute n(A), n(B), n(A and B) and n(A or B)

The union of A & B has 48 elements. Set A contains 27 elements. Set B contains 30 elements. How many elements are in the intersection of A & B?

Evaluate P(4, 3) WITHOUT a calculator.

Eight guys are candidates for the “Big Man on Campus” competition. In how many ways can 1 st, 2 nd, and 3 rd place be awarded?

In how many ways can the letters of the word REARRANGE be permuted?

A = {a, b, c, d, e, f, g, x, y, z} B = {c, r, a, z, y} Find … n(A), n(B), n(A and B), n(A or B)

Two sets are formed using 100 elements. There are 60 elements in one set and 75 in the other. How many sets are in the intersection of the two sets?

If a universal set contains 500 elements, n(A) = 240, n(A or B) = 460, n(A & B) = 55. Find n(B’).

Given two sets A and B where n(A) = 5, n(B) = 10 and n(A or B) = 15. Find the intersection of A and B. What is the intersection of A and B?

Charlie interviewed 135 students for his Sociology project: 65 said they like to go to the movies 77 said they like to go to football games 61 said they like to go to the theater 28 said they like movies & football games 25 said they like movies & the theater 29 said they like to attend football games & the theater 8 said they like to attend all three 4 said they don’t like to attend any of them The professor refused to accept Charlie’s paper because the information was inconsistent. Was the professor justified in claiming the information was inconsistent?

Professor Sendon and Professor Barr were comparing their class rolls. They observed that Professor Sendon had 28 students, Professor Barr had 21 students, and 4 students were enrolled in both classes. If they held a joint meeting of their classes and all students attend, how many students are present?

The Student Life Committee asks that 2 members from a service club attend the next committee meeting. The two students will be selected from one of the following service clubs: Alpha Club with 22 members, Beta Club with 19 members, Gamma Club with 25 members, and Zeta Club with 14 members. In how many ways can the 2 students be selected?

A committee of 5 people is selected from a group of 6 men and 7 women. In how many ways can the committee be selected so it contains at least one woman?

An Honor Council consists of 4 seniors, 4 juniors, 3 sophomores, and 1 freshman. 15 seniors, 20 juniors, 25 sophomores, and 11 freshman apply. In how many ways can the Honor Council be selected?

How many different words are possible using all the letters of the letters of … … RELAX? … PUPPY? … OFFICIAL?