Exam 11: Sequences, Series, and Probability

The numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 are to be arranged. How many different arrangements are possible under the condition that all odd numbers come first?

Determine the sample space for the experiment. Three prize winners are selected from six people: A, B, C, D, E, and F.

Eight cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if three or more cards are kings.

Use the Binomial Theorem to simplify the power of the complex number.

A state lottery game requires a person to select six different numbers from thirty-seven numbers. The order of the selection is not important. In how many ways can this be done?

A letter listing the names and addresses of 8 people was sent to 3 other people, who were asked to send $5 to the name at the top of the list and then remove that person's name. Each recipient then added his or her name to the bottom of the list and sent the letter to five friends. Assuming no one broke the chain, how much money would each recipient of the letter receive?

Nineteen students are selected as semifinalists for a literary award. Of the nineteen students, ten finalists will be selected. In how many ways can ten finalists be selected from the nineteen students?

A club has nine members. One member starts a rumor by telling it to a second club member, who repeats the rumor to a third member, and so on. At each stage, the recipient of the rumor is chosen at random from the nine club members. What is the probability that the rumor will be told eight times without returning to the originator? Round to the nearest hundredth.

Find the sum of the finite geometric series. Round to the nearest hundredth.

Find the third term of the sequence that has the given n th term.

Seven cards are chosen at random from a standard deck of playing cards. In how many ways can the cards be chosen if all seven cards are the same suit.

Use the Binomial Theorem to expand and simplify the expression.

A single number is chosen from the digits 1, 2, 3, 4, 5, and 6. Find the probability that the number is an odd number or a number divisible by 3.

Nine weightlifters are competing in the dead-lift competition. In how many ways can the weightlifters finish first, second, and third (no ties)?

The seating section in a theater has 29 seats in the first row, 34 seats in the second row, and so on, increasing by 5 seats each row for a total of 13 rows. How many seats are in the tenth row?

A quality control inspector receives a shipment of 20 computer monitors. From the 20 monitors, the inspector randomly chooses 6 for inspection. If the probability of a monitor being defective is 0.12, what is the probability that at least one of the monitors chosen by the inspector is defective? Round to the nearest hundredth.

An airline estimates that 80% of the people who make a reservation for a certain flight will actually show up for the flight. Suppose the airline sells 22 tickets on this flight and the plane has room for 18 passengers. What is the probability that 19 or more people with tickets will show up for the flight? Round to the nearest hundredth.

Twenty-three students, of whom ten are seniors, are selected as semifinalists for a literary award. Of the twenty-three students, thirteen finalists will be selected. In how many ways can the thirteen finalists contain at least four seniors?

Find the seventh term of the sequence that has the given nth term below. is the digit in the nth place in the decimal expansion of .

Twenty-eight students, of whom seven are seniors, are selected as semifinalists for a literary award. Of the twenty-eight students, fourteen finalists will be selected. In how many ways can the fourteen finalists contain five seniors?