Exam 4: Probability and Counting Rules

There are four instructors, nine assistant professors, and five associate professors in the Math department. A committee of five is selected to choose new textbooks. There are 1,440 ways that a committee can be selected, if there must be one instructor, two assistant professors, and two associate professors on the committee.

How many ways can a student select five questions from an exam containing 12 questions, if one of the five must be the last question?

How many possible outcomes would there be if three coins were tossed once?

If the letters A, B, C, D, E, and F are to be used in a five-letter code, how many different codes are possible if repetitions are not permitted?

Given the following Venn diagram, which of the following equations could be used to calculate the probability of either event A, event B, or event C occurring.

There are 3 blue balls, 5 red balls, and 4 white balls in a bag of balls. If a person selects two of the balls, what is the probability that the second one is blue given that the first one was white?

Evaluate the following: ₇P₃.

A group of 6 children are choosing colored pencils to draw a picture. Each child is allowed to select one color. The available colors are green, red, and blue. If the second child refuses to use red pencils and the third child refuses to use blue pencils, then how many ways are there for the children to choose pencils? Assume that there are 12 pencils available of each color, and different children are allowed to choose the same color.

If a red suit is drawn from an ordinary deck of cards, what is the probability that the card is a diamond?

Each of 8 students wishes to buy a particular textbook, but only 5 textbooks are available. How could one express the number of ways those textbooks could be distributed among the students?

A recent poll found that 30% of those surveyed are worried about aggressive drivers on the road. If three people are selected at random, what is the probability that all three will be worried about aggressive drivers on the road?

It has been reported that 3% of all cars on the highway are traveling at speeds in excess of 70 mph. If the speeds of four random automobiles are measured via radar, what is the probability that at least one car is going over 70 mph?

At Wassamatta University, 55.7% of the student body are males. Choose one student at random. What is the probability that the student is female?

A single card is drawn from a deck. Find the probability of selecting a heart or a 9.

The staff at a small company includes: 4 secretaries, 20 technicians, 4 engineers, 2 executives, and 50 factory workers. If a person is selected at random, what is the probability that he or she is a factory worker?

A student and a professor each choose a number between 1 and 6 (1 and 6 are both possible choices). What is the probability that the two choose the same number?

What type of probability uses a knowledge of sample spaces as opposed to experiments to determine the numerical probability that an event will occur?

How many different ways can a teacher select 5 students from a class of 19 students to each perform a different classroom task?

How many different ways can four people: Andy, Betty, Cindy, and Doug, sit in a row at the opera if Andy and Betty must sit together?

A store manager wants to display 4 different brands of toothpaste in a row. How many ways can this be done?