CHAPTER 1
1. How many different linear arrangements are there of the letters A, B, C, D,
E, F for which
(a) A and B are next to each other;
(b) A is before B;
(c) A is before B and B is before C;
(d) A is before B and C is before D;
(e) A and B are next to each other and C and D are also next to each other;
(t) E is not last in line?
2. If 4 Americans, 3 Frenchmen, and 3 Englishmen are to be seated in a row, how many seating arrangements are possible when people of the same national ity must sit next co each other?
3. A president, treasurer, and secretary, all different, are to be chosen from a club consisting of 10 people. How many different choices of officers are possible if
(a) there are no restrictions;
(b) A and B will not serve together;
(c) C and D Will serve together or not at all;
(d) E must be an officer;
(e) F will serve only if he is president?
4. A student is to answer 7 out of 10 questions in an examination. How many choices has she? How many if sbe must answer at least 3 of the first 5 ques tions?
5. In how many ways can a man divide 7 gifts among his 3 children if the eldest is to receive 3 gifts and the others 2 each?
6. How many different 7-place license plates are possible when 3 of the entries are letters and 4 are digits? Assume that repetition of letters and numbers is allowed and that there is no restriction on where the letters or numbers can be placed.
Chapter 2
1. A cafeteria offers a 3-course meal. One chooses an entree, a starch, and a dessert. The possible choices are given below.
Course Choices
Entree
Starch
Dessrt
Chicken or roast beef
Pasta or rice or potatoes
Ice cream or Jello or apple pie or a peach
A person is to choose one course from each category.
(a) How many outcomes are in the sample space?
(b) Let A be the event that ice cream is chosen. How many outcomes are in A?
(c) Let B be the event that chicken is chosen. How many outcomes are in B?
(d) List all tpe outcomes in the event AB.
(e) Let 0’be the event that rice is chosen. How many outcomes are in C?
(f) List all the outcomes in the event ABC.
2. A customer visiting the suit department of a certain store will purchase a suit with probability.22, a shirt with probability.30, and a tie with probability
.28. The customer will purchase both a suit and a shirt with probability.11, both a suit and a tie with probability.14, and both a shirt and a tie with probability.10. A customer will purchase all 3 items with probability.06.
What is the probability that a customer purchases
(a) none of these items;
(b) exactly I of these items?
3. A deck of cards is dealt out. What is the probability that the fourteenth card dealt is an ace? What is the probability that the first ace occurs on the fourteenth card?
4. Let A denote the event that the midtown temperature in Los Angeles is 70°F, and let B denote the event that the midtown temperature in New York is 70°F. Also, let C denote the event that the maximum of the midtown temperatures in New Yqrk and in Los Angeles isJO:’.F. If P(A) =.3, P(B) =.4, and P(C) =.2, find the probability that the minimum of the two皿dtown tempera tures is 70°F.