1. There are four routes A, B, C and it), between a person's home and the place where he works, but route 3 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. nd the number of ways the person can go to and from work. {b} By drawing a tree diagram, nd the number of ways he can go to and from work without taking the same route both ways. 2. Amy has It] ditferent mathematics books and 8 dilferent chemistry books. In how many ways can she (a) put all 13 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 lled (a) with any 2 of the T nominees; {h} with any 2 of the 4 women; {c} with one of the men and one of the women