1. There are 15 questions on a multiple-choice exam and five possible answers to
ID: 2903116 • Letter: 1
Question
1. There are 15 questions on a multiple-choice exam and five possible answers to each question.
a. In how many ways can the exam be answered?
b. In how many ways can the exam be answered with exactly eight answers correct?
2. A florist sells roses in five different colors.
a. How many bunches of a half-dozen roses can be formed?
b. How many bunches of a half-dozen can be formed if each bunch must contain at least one rose of each color
3.
a. In how many ways can five different mathematics books, three different physics books, and four different chemistry books be arranged on a shelf?
b. Repeat (a) if all books of the same subject are to be together.
c. Repeat (a) if three of the five mathematics books are the same.
d. Repeat (c) if, in addition, all the physics books are the same.
4. In how many ways can 18 different books be given to Tara, Danny, Shannon, and Mike so that one person has six books, one has two books, and the other two people have five books each?
5. Find the number of arrangements of the letters of each of the following words:
a. SCIENTIFIC
b. SASKATOON
c. PICCINNI
d. CINCINNATI
6. In a university residence there are five single rooms, five double, and five rooms that hold three students each. In how many ways can 30 students be assigned to the 15 rooms? (All rooms are numbered.)
Explanation / Answer
1.
a. In how many ways can the exam be answered?
Ans: 15^5.
b. In how many ways can the exam be answered with exactly eight answers correct?
Ans: 15C8*7^5.
.2. A florist sells roses in five different colors.
a. How many bunches of a half-dozen roses can be formed?
Ans: 6^5.
b. How many bunches of a half-dozen can be formed if each bunch must contain at least one rose of each color
Ans: 5.
3.
a. In how many ways can five different mathematics books, three different physics books, and four different chemistry books be arranged on a shelf?
Ans: 12!
b. Repeat (a) if all books of the same subject are to be together.
Ans:3!*5!*3!*4!
c. Repeat (a) if three of the five mathematics books are the same.
Ans: 12!/3!
d. Repeat (c) if, in addition, all the physics books are the same.
Ans: 3!*5!*4!
4. In how many ways can 18 different books be given to Tara, Danny, Shannon, and Mike so that one person has six books, one has two books, and the other two people have five books each?
Ans:18C6*12C2*10C5
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