1.(A) How many ways can a 4-person subcommittee be selected from a committee of

6 people?

(B) How many ways can a president,vice-president,secretary,andtreasurer

be chosen from a committee of 6 people?

2.A paint store carriesfifteen brands of paint. A customer wants to buy another gallon of paint to match paint she purchased at the store recently. Shecan't recall the brand name and does not wish to return home to find the old can of paint. So she selectstwo of thefifteen brands at random and buys them.

a.Her husband also goes to the paint store and fails to remember what brand to buy. So he also purchasestwo of thefifteen brands of paint at random. Determine the probability that both the woman and her husband fail to get the correct brand of paint.(Hint: Are thehusband's selections independent of hiswife's selections?)

3.A small hotel in a popular resort area has25 rooms. The hotel manager estimates that

13% of all confirmed reservations are"no-shows." Consequently, the hotel accepts confirmed reservations for as many as30 rooms. If more confirmed reservations arrive than there arerooms, the overbooked guests are sent to another hotel and given a complementary dinner. Complete parts a through c below assuming that the hotel currently has30 confirmed reservations.

a.Find the probability that no customers will be sent to another hotel.

b.Find the probability that exactly1 guest will be sent to another hotel.

c.Find the probability that2 or more guests will be sent to another hotel.

4.A company has threeblack-and-white copy machines and two color copiers. Based on historicaldata, the chance that eachblack-and-white copier will be down for repairs is0.05. The color copiers are more of a problem and are down24% of the time each. Complete parts a through d below.

a. Based on thisinformation, what is the probability that if a customer needs a colorcopy, both color machines will be down forrepairs?

b. If a customer wants both a color copy and ablack-and-white copy, what is the probability that the necessary machines will beavailable? (Assume that the color copier can also be used to make ablack-and-white copy ifneeded.)

c.If the manager wants to have at least a99% chance of being able to furnish ablack-and-white copy ondemand, is the present configurationsufficient? (Assume that the color copier can also be used to make ablack-and-white copy ifneeded.) Back up your answer with appropriate probability computations.

d)What is the probability that all five copiers will be up and running at the sametime?

5.Radio frequency identification(RFID) is an electronic scanning technology that can be used to identify items in a number of ways. One advantage of RFID is that it can eliminate the need to manually countinventory, which can help improve inventory management. The technology is notinfallible, however, and sometimes errors occur when items are scanned. The probability that a scanning error occurs is

0.006. Complete parts a through d.

a. Find the probability that exactly22 items will be scanned incorrectly from the next

5,100 items scanned.

b.Find the probability that more than 22 items will be scanned incorrectly from the next5,100 items scanned.

c.Find the probability that the number of items scanned incorrectly is between 15 and22, inclusive, from the next5,100 items scanned.

d.Find the expected number of items scanned incorrectly from the next 5,100 items scanned.