Officers The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 14 candidates. Six of the candidates are members of the debate team.
b. What is the probability that none of the offices are filled by members of the debate team?

34. Lottery Number Selection A lottery has 52 numbers. In how many different ways can six of the numbers be selected? (Assume the order of selection is not important.)

37. Water Pollution An environmental agency is analyzing water samples from 80 lakes for pollution. Five of the lakes have dangerously high levels of dioxin. Six lakes are randomly selected from the sample. Use technology to find how many ways one polluted lake and five nonpolluted lakes can be chosen.

Board of Directors The University of Colorado Board of Directors has 23 members. One member serves as board chair and another serves as vice chair. Given the names of the 23

board members, what is the probability of randomly selecting the name of the chair and the name of the vice chair? (Source: University of Colorado)

Shuffle Play You use a shuffle playback feature to randomly play songs in a playlist. The playlist of 56 songs includes 15 instrumental songs.

a. What is the probability that the first three songs to play are instrumental songs? (Assume a song cannot be repeated.)

50. Investment Committee A company has 200 employees, consisting of 144 women and 56 men. The company wants to select five employees to serve as an investment committee.

d. Explain how the company can select a representative sample of the male and female population of employees.

Warehouse In Exercises 51-54, a warehouse employs 24 workers on first shift, 17 workers on second shift, and 13 workers on third shift. Eight workers are chosen at random to be

interviewed about the work environment.

Find the probability of choosing four third-shift workers.

56. Defective Disks A pack of 100 recordable DVDs contains 5 defective disks. You select four disks. What is the probability of selecting at least three non defective disks?

Cards In Exercises 59-62, you are dealt a hand of five cards from a standard deck of 52 playing cards.

59. Find the probability of being dealt two clubs and one of each of the other three suits.