1. There are four routes A, B, C and D, between a person's home and the place where he works, but route B is one-way, so he cannot take it on the way to work, and route C is one-way, so he cannot take it on the way home. (a) By drawing a tree diagram, find the number of ways the person can go to and from work. (b) By drawing a tree diagram, find the number of ways he can go to and from work without taking the same route both ways. 2. Amy has 10 different mathematics books and 8 different chemistry books. In how many ways can she (a) put all 18 books on a shelf? (b) put 6 books on a shelf? (c) put half of the math and half othe chemistry books on a shelf, with the math books all to the left of the chemistry books? 3. Among the seven nominees for two vacancies on a city council are 3 men and 4 women. In how many ways can these vacancies be filled (a) with any 2 of the 7 nominees; (b) with any 2 of the 4 women; (c) with one of the men and one of the women?
1. There are four routes A, B, C and D, between a person's home and the place where he works, but route B is one-way, so he cannot take it on the way to work, and route C is one-way, so he cannot take it on the way home. (a) By drawing a tree diagram, find the number of ways the person can go to and from work. (b) By drawing a tree diagram, find the number of ways he can go to and from work without taking the same route both ways. 2. Amy has 10 different mathematics books and 8 different chemistry books. In how many ways can she (a) put all 18 books on a shelf? (b) put 6 books on a shelf? (c) put half of the math and half othe chemistry books on a shelf, with the math books all to the left of the chemistry books? 3. Among the seven nominees for two vacancies on a city council are 3 men and 4 women. In how many ways can these vacancies be filled (a) with any 2 of the 7 nominees; (b) with any 2 of the 4 women; (c) with one of the men and one of the women?
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...
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Transcribed Image Text:1. There are four routes A, B, C and D, between a person's home and the place where he works, but
route B is one-way, so he cannot take it on the way to work, and route C is one-way, so he cannot
take it on the way home.
(a) By drawing a tree diagram, find the number of ways the person can go to and from work.
(b) By drawing a tree diagram, find the number of ways he can go to and from work without
taking the same route both ways.
2. Amy has 10 different mathematics books and 8 different chemistry books. In how many ways can
she
(a) put all 18 books on a shelf?
(b) put 6 books on a shelf?
(c) put half of the math and half othe chemistry books on a shelf, with the math books all to the
left of the chemistry books?
3. Among the seven nominees for two vacancies on a city council are 3 men and 4 women. In how
many ways can these vacancies be filled
(a) with any 2 of the 7 nominees;
(b) with any 2 of the 4 women;
(c) with one of the men and one of the women?
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