Читать книгу Statistics and Probability with Applications for Engineers and Scientists Using MINITAB, R and JMP - Bhisham C. Gupta, Irwin Guttman - Страница 124

1 In a certain clinical trial, a medical team wants to study four different doses of a new medication for cervical cancer in five patients. In how many different ways can the team select one dose of the medication and one of the patients?

2 A small motel with nine rooms has three twin beds in two rooms, two twin beds in three rooms, and one twin bed in rest of the four rooms. In how many different ways can the manager of the motel assign these rooms to a group of 16 guests who told the manager that they have no preference about whom they share the room with?

3 In how many ways can a class of 30 students select a committee from the class that consists of a president, a vice president, a treasurer, and a secretary (a) if any student may serve either of these roles but no student may serve in multiple roles and (b) if any student may serve in multiple roles?

4 A multiple‐choice board exam consists of 15 questions, each question having four possible answers. In how many different ways can a candidate select one answer to each question?

5 A chain restaurant offers a dinner menu with four different soups, three different salads, 10 entrees, and four desserts. In how many ways can a customer choose a soup, a salad, an entrée, and a dessert?

6 If in Problem 3 above, the committee consists of just four members, then in how many ways can the class select the committee?

7 If 13 cards are dealt from a thoroughly shuffled deck of 52 ordinary playing cards, find the probability of getting five spades and four diamonds.

8 How many different permutations can be obtained by arranging the letters of the word engineering? Cardiologist?

9 A cholesterol‐lowering drug is manufactured by four different pharmaceutical companies in five different strengths and two different forms (tablet and capsule). In how many different ways can a physician prescribe this drug to a patient?

10 How many different car plates can be issued if the Department of Motor Vehicles decides to first use two letters of the English alphabet and then any four of the digits ?

11 In a random experiment, one die is rolled, one coin is tossed, and a card is drawn from a well‐shuffled regular deck of playing cards and its suit noted. How many sample points are there in the sample space of this random experiment?

12 Each of 10 websites either contains (C) an ad of a car manufacturer or does not contain the ad (N). How many sample points are there in the sample space of a random experiment that selects a website at random?