Chapter 14

A parcel delivery truck can take any one of 3 different roads from Clarksville to Leesville and any one of 4 different roads from Leesville to Jonesboro. How many different routes are available from Clarksville to Jonesboro?

A car can be ordered in any one of 8 different colors, with 3 different engine sizes, 2 different transmissions, 3 different body styles, 4 different interior designs, and 5 different stereos. How many different cars are available?

Solve each probability problem. If a single die is tossed, then what is the probability of getting a) a number larger than 3? b) a number less than or equal to 5? c) a number other than 6? d) a number larger than 7? e) a number smaller than 9?

A certain card game consists of 3 cards drawn from a poker deck of \(52 .\) How many different 3 -card hands are there containing one heart, one diamond, and one club?

If a pair of coins is tossed, then what is the probability of getting a) exactly two heads? b) at least one tail? c) exactly two tails? d) at most one tail?

Wendy's Hamburgers once advertised that there were 256 different hamburgers available at Wendy's. This number was obtained by using the fundamental counting principle and considering whether to include each one of several different options on the burger. How many different optional items were used to get this number?

If a single coin is tossed twice, then what is the probability of getting a) heads followed by tails? b) two heads in a row? c) a tail on the second toss? d) exactly one tail?

A pizza can be ordered with your choice of one of 4 different meats or no meat. You also have a choice of whether to include green peppers, onions, mushrooms, anchovies, or black olives. How many different pizzas can be ordered?

Solve each problem. See Examples 1 and 2 . The water inspector in drought-stricken Marin County randomly selects 10 homes for inspection from a list of 25 suspected violators of the rationing laws. How many ways are there to pick the 10 homes?

If a pair of dice is tossed, then what is the probability of getting a) a pair of 2’s? b) at least one 2? c) a sum of 7? d) a sum greater than 1? e) a sum less than 2?

Randall has homework in mathematics, history, art, literature, and chemistry but cannot decide in which order to attack these subjects. How many different orders are possible?

Solve each problem. See Examples 1 and 2 . In the Florida Lottery you can win a lot of money for merely selecting 6 different numbers from the numbers 1 through 49. How many different ways are there to select the 6 numbers?

If a single die is tossed twice, then what is the probability of getting a) a 1 followed by a 2? b) a sum of 3? c) a 6 on the second toss? d) no more than two 5’s? e) an even number followed by an odd number?

Yesha has 12 schools to visit this week. In how many different ways can she pick a first, second, and third school to visit on Monday?

A ball is selected at random from a jar containing 3 red balls, 4 yellow balls, and 5 green balls. What is the probability that a) the ball is red? b) the ball is not yellow? c) the ball is either red or green? d) the ball is neither red nor green?

In how many ways can a history professor randomly assign exactly one \(\mathrm{A},\) one \(\mathrm{B},\) one \(\mathrm{C},\) one \(\mathrm{D},\) and \(\operatorname{six} \mathrm{F}^{\prime}\) s to a class of 10 students?

A committee consists of 1 Democrat, 5 Republicans, and 6 independents. If one person is randomly selected from the committee to be the chairperson, then what is the probability that a) the person is a Democrat? b) the person is either a Democrat or a Republican? c) the person is not a Republican?

The program director for an independent television station has 34 one-hour shows available for Monday night prime time. How many different schedules are possible for the 7: 00 to 10: 00 P.M. time period?

A jar contains 10 balls numbered 1 through 10. Two balls are randomly selected one at a time without replacement. What is the probability that a) 1 is selected first and 2 is selected second? b) the sum of the numbers selected is 3? c) the sum of the numbers selected is 6?

A disc jockey must choose 8 songs from the top 40 to play in the next 30 -minute segment of his show. How many different arrangements are possible for this segment?

A small company consists of a president, a vice-president, and 14 salespeople. If 2 of the 16 people are randomly selected to win a Hawaiian vacation, then what is the probability that none of the salespeople is a winner?

How many different ways are there to mark the answers to a 20 -question multiple-choice test in which each question has 4 possible answers?

If a 5-card poker hand is drawn from a deck of 52, then what is the probability that a) the hand contains the ace, king, queen, jack, and ten of spades? b) the hand contains one 2, one 3, one 4, one 5, and one 6?

A bookstore manager wants to make a window display that consists of a mathematics book, a history book, and an economics book in that order. He has 13 different mathematics books, 10 different history books, and 5 different economics books from which to choose. How many different displays are possible?

If 5 people with different names and different weights randomly line up to buy concert tickets, then what is the probability that a) they line up in alphabetical order? b) they line up in order of increasing weight?

In how many ways can the 37 seats on a commuter flight be filled from the 39 people holding tickets?

Use the addition rule to solve each problem. Among the drivers insured by American Insurance, 65% are women, 38% of the drivers are in a high-risk category, and 24% of the drivers are high-risk women. If a driver is randomly selected from that company, what is the probability that the driver is either high-risk or a woman?

If a couple has decided on 6 possible first names for their baby and 5 possible middle names, then how many ways are there for them to name their baby?

What is the probability of getting either a sum of 7 or at least one 4 in the toss of a pair of dice?

A developer builds houses with 3 different exterior styles. You have your choice of \(3,4,\) or 5 bedrooms, a fireplace, 2 or 3 baths, and 5 different kitchen designs. How many different houses are available?

A couple plans to have 3 children. Assuming males and females are equally likely, what is the probability that they have either 3 boys or 3 girls?

How many different seven-digit phone numbers are available in Wentworth if the first three digits must be \(286 ?\)

What is the probability of getting a sum of 10 or a sum of 5 in the toss of a pair of dice?

Solve each problem. See Examples \(3-5\) For her final exam in Literature 302 Charlotte is allowed to omit any 5 of the 8 essay questions. How many ways are there for her to omit the 5 questions?

How many different seven-digit phone numbers are available in Creekside if the first digit cannot be a \(0 ?\)

What is the probability of getting either a heart or an ace when drawing a single card from a deck of 52 cards?

In how many different ways can a Mercedes, a Cadillac, and a Ford be awarded to 3 people chosen from the 9 finalists in a contest?

What is the probability of getting either a heart or a spade when drawing a single card from a deck of 52 cards?

Solve each problem. See Examples \(3-5\) How many distinct triangles are determined by 5 points lying on a circle, where the vertices of each triangle are chosen from the 5 points?

How many different ways are there to seat 7 students in a row?

If the probability of surviving a head-on car accident at 55 mph is 0.005, then what is the probability of not surviving?

A supply boat must stop at 9 oil rigs in the Gulf of Mexico. How many different routes are possible?

If the probability of a tax return not being audited by the IRS is 0.97, then what is the probability of a tax return being audited?

How many different license plates can be formed by using 3 digits followed by a single letter followed by 3 more digits? How many if the single letter can occur anywhere except last?

A pair of dice is tossed. What is the probability of a) getting a pair of 4’s? b) not getting a pair of 4’s? c) getting at least one number that is not a 4?

Solve each problem. See Examples \(3-5\) The outcome "heads" or "tails" is recorded on each toss of a coin. If we think of the outcome for 3 tosses as an ordered triple, then how many outcomes are there for 3 tosses of a coin?

How many different license plates can be formed by using any 3 letters followed by any 3 digits? How many if we allow either the 3 digits or the 3 letters to come first?

Three coins are tossed. What is the probability of a) getting three heads? b) not getting three heads? c) getting at least one tail?

Make a list of all of the subsets of the set \(\\{a, b, c\\} .\) How many are there?

If the probability is 60% that the eye of Hurricane Edna comes ashore within 30 miles of Charleston, then what are the odds in favor of the eye of Edna coming ashore within 30 miles of Charleston?