3. A train to the western frontier will consist of 4 passenger cars, 3 cattle cars, and 2 luggage cars, which are to be

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3 A Train To The Western Frontier Will Consist Of 4 Passenger Cars 3 Cattle Cars And 2 Luggage Cars Which Are To Be 1 (44.97 KiB) Viewed 93 times

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 Indy'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? (e) 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? () 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?