Solve the problem.There are 5 women running in a race. If a person guesses randomly the first place, second place, and third place winners, what is the probability that they will guess all winners correctly?

Solve the problem.A tourist in France wants to visit 11 different cities. If the route is randomly selected, what is the probability that she will visit the cities in alphabetical order?

A game consists of laying a $1 bet and taking a single card from a dealer (the house) working with a 54-card deck, which includes two jokers. If the card is clubs, the player gets their $1 back and wins an additional $3. If the card is not clubs, the player loses their $1 bet. What is the house edge (the expected value to the house)?

Solve the problem.A license plate is to consist of 2 letters followed by 4 digits. Determine the number of different license plates possible if repetition of letters and numbers is not permitted.

Solve the problem.8 basketball players are to be selected to play in a special game. The players will be selected from a list of 27 players. If the players are selected randomly, what is the probability that the 8 tallest players will be selected?

Solve the problem.How many different 4-topping pizzas can be made if there are 8 individual toppings to choose from? Assume that no topping is used more than once and that the order of the toppings on the pizza is unimportant.

Find the expected value.Suppose you pay $3.00 to roll a fair (6-sided) die with the understanding that you will get back $5.00 for rolling a 1 or a 5, nothing otherwise. What is your expected net winnings?

Solve the problem.In a certain lottery, 3 different numbers between 1 and 8 inclusive are drawn. These are the winning numbers. How many different selections are possible? Assume that the order in which the numbers are drawn is unimportant.

Solve the problem.How many different 6-letter sequences can be made using the first 11 letters of the alphabet? Assume that repetition of letters is allowed.

Find the expected value.The following table gives the distribution of heights for female students at one U.S. college. Distribution of heights HEIGHT CATEGORY (INCHES) PERCENTAGE 57 – 59 7.8% 60 – 62 19.4% 63 – 65 37.5% 66 – 68 19.6% 69 – 71 11.0% 72 and older 4.7% Find the expected value of height for women at this college. Use the midpoint of each category, (for example use 58 for the 57-59 category). Use 74 for the 72 and over category.