3. A train to the western frontier will consist of 4 passenger cars, 3 cattle cars, and 2 luggage cars, which are to be put in order at random. (a) Bandits plan to mount the train and enter the two rearmost cars. Find the probability that they enter i. two passenger cars. ii. a luggage car and a passenger car. iii. at least one cattle car. (b) A lady's shawl flies out a window of the foremost passenger car, reenters a window in the rearmost passenger car, and is seized by a gentleman who gallantly vows to return it while the train is in motion. With what probability can he make his way from the rearmost passenger car to the foremost, passing only through passenger cars? (c) There are 14 head of cattle to be transported in the three cattle cars. i. In how many ways can 5, 5, and 4 head of cattle, respectively, be put into the three cattle cars? ii. The gallant gentleman owns 3 of the 14 head of cattle. If 5, 5, and 4 of the 14 head of cattle are put into the three cattle cars at random, with what probability will the gallant gentleman's cattle all be placed in the same cattle car? (d) Mr. and Mrs. Wilkins and their two daughters and three sons are boarding one of the passenger cars on the next stop. i. In how many different orders can the members of the Wilkins family enter the car? ii. In how many of these orders does Mrs. Wilkins precede Mr. Wilkins? iii. In how many of these orders does Mrs. Wilkins and her two daughters precede Mr. Wilkins his three sons? (e) At each of the 10 stops along Lil' Jonnie's journey on the train, he will decide whether to quickly hop out and scrawl his initials somewhere around the station or to remain on board. At how many unique sets of stations can Lil' Jonnie scrawl his initials?
3. A train to the western frontier will consist of 4 passenger cars, 3 cattle cars, and 2 luggage cars, which are to be put in order at random. (a) Bandits plan to mount the train and enter the two rearmost cars. Find the probability that they enter i. two passenger cars. ii. a luggage car and a passenger car. iii. at least one cattle car. (b) A lady's shawl flies out a window of the foremost passenger car, reenters a window in the rearmost passenger car, and is seized by a gentleman who gallantly vows to return it while the train is in motion. With what probability can he make his way from the rearmost passenger car to the foremost, passing only through passenger cars? (c) There are 14 head of cattle to be transported in the three cattle cars. i. In how many ways can 5, 5, and 4 head of cattle, respectively, be put into the three cattle cars? ii. The gallant gentleman owns 3 of the 14 head of cattle. If 5, 5, and 4 of the 14 head of cattle are put into the three cattle cars at random, with what probability will the gallant gentleman's cattle all be placed in the same cattle car? (d) Mr. and Mrs. Wilkins and their two daughters and three sons are boarding one of the passenger cars on the next stop. i. In how many different orders can the members of the Wilkins family enter the car? ii. In how many of these orders does Mrs. Wilkins precede Mr. Wilkins? iii. In how many of these orders does Mrs. Wilkins and her two daughters precede Mr. Wilkins his three sons? (e) At each of the 10 stops along Lil' Jonnie's journey on the train, he will decide whether to quickly hop out and scrawl his initials somewhere around the station or to remain on board. At how many unique sets of stations can Lil' Jonnie scrawl his initials?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Transcribed Image Text:3. A train to the western frontier will consist of 4 passenger cars, 3 cattle cars, and 2 luggage cars,
which are to be put in order at random.
(a) Bandits plan to mount the train and enter the two rearmost cars. Find the probability that
they enter
i. two passenger cars.
ii. a luggage car and a passenger car.
iii. at least one cattle car.
(b) A lady's shawl flies out a window of the foremost passenger car, reenters a window in the
rearmost passenger car, and is seized by a gentleman who gallantly vows to return it while the
train is in motion. With what probability can he make his way from the rearmost passenger
car to the foremost, passing only through passenger cars?
(c) There are 14 head of cattle to be transported in the three cattle cars.
i. In how many ways can 5, 5, and 4 head of cattle, respectively, be put into the three cattle
cars?
ii. The gallant gentleman owns 3 of the 14 head of cattle. If 5, 5, and 4 of the 14 head of
cattle are put into the three cattle cars at random, with what probability will the gallant
gentleman's cattle all be placed in the same cattle car?
(d) Mr. and Mrs. Wilkins and their two daughters and three sons are boarding one of the passenger
cars on the next stop.
i. In how many different orders can the members of the Wilkins family enter the car?
ii. In how many of these orders does Mrs. Wilkins precede Mr. Wilkins?
iii. In how many of these orders does Mrs. Wilkins and her two daughters precede Mr. Wilkins
his three sons?
(e) At each of the 10 stops along Lil' Jonnie's journey on the train, he will decide whether to
quickly hop out and scrawl his initials somewhere around the station or to remain on board.
At how many unique sets of stations can Lil' Jonnie scrawl his initials?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON