Discret Math 2 cont.

Multiple Select

Which one is an example of a permutation

• Arranging the competition winners' positions

• Creating a password or PIN

• Arranging seats

• Taking a card

• Choosing clothes

Multiple Select

Which one is an example of a combination

• Choosing a team

• Choosing a food menu

• Queue order

• Taking a card

Multiple Select

Among 10 students of the 2013 Informatics Engineering batch (named A, B, C, .., H, I, J), how many ways are there to form a 5-member representative group such that:

(a) the student named A is always included;

(b) the student named A is not included;

• 126

• 70

• 56

• 196

Multiple Select

Among 10 students of the 2013 Informatics Engineering batch (named A, B, C, .., H, I, J), how many ways are there to form a 5-member representative group such that:

(c) the student named A is always included in it, but B is not;

(d) the student named B is always included in it, but A is not;

• 126

• 70

• 56

• 196

Multiple Select

Among 10 students of the 2013 Informatics Engineering batch (named A, B, C, .., H, I, J), how many ways are there to form a 5-member representative group such that:

(e) students named A and B are included in it;

(f) at least one of the students named A or B is included in it.

• 126

• 70

• 56

• 196

Multiple Choice

A teacher has 4 female students and 3 male students who are all

under 17 years old. The teacher wants to take her students to a restaurant.

Because the teacher's car can only accommodate 5 people including herself, only

4 of her students can ride in her car. The teacher needs at least one boy in her car

to accompany her as a guide. In how many ways can the teacher choose which

students to take to the restaurant?

• 25

• 34

• 33

• 30

Multiple Choice

1. A restaurant provides five types of food, for example

fried rice, bread, chicken soto, satay, and soup, and

three types of drinks, for example milk, coffee, and tea.

If each person is allowed to order one food and one

drink, how many food and drink pairs can be ordered?

• 13

• 14

• 15

• 16

Multiple Choice

2. The position of chairman of the association can be

filled by students from the 2012 or 2013 intake. If there

are 45 students from the 2012 intake and 52 students

from the 2013 intake, how many ways can the acting

chairman of the association be chosen?

• 87

• 92

• 97

• 100

Multiple Choice

3. group of students consists of 4 men and 3 women.

How many ways are there to choose one male

representative and one female representative?

• 12

• 7

• 8

• 5

Multiple Choice

4. A group of students consists of 4 men and 3 women.

How many ways are there to choose one person to

represent the group (regardless of whether male or

female)?

• 7

• 12

• 15

• 21

Multiple Choice

5. he chairs in the auditorium are numbered with a

letter followed by a positive integer not exceeding 50

(e.g. A26, B36, and so on). What is the maximum

number of chairs that can be numbered?

• 1300

• 1200

• 50

• 26

Multiple Choice

6a. here are four routes that can be taken by vehicles from

Mataram to Praya, and three routes from Praya to Selong.

How many ways can a person travel by vehicle from Mataram to

Selong via Praya?

• 12

• 144

• 30

• 24

Multiple Choice

6b. here are four routes that can be taken by vehicles from

Mataram to Praya, and three routes from Praya to Selong.

How many ways can a person travel round trip by vehicle from

Mataram to Selong via Praya?

• 12

• 144

• 20

• 36

Multiple Choice

7 If there are five questions that can each be answered true or

false (T or F), how many possible combinations of answers canbe made?

• 7

• 32

• 14

• 16

Multiple Choice

8a. A library has 6 English books, 8 French books, and 10 German books. Each book

has a different title. How many ways can you choose:

Three books, one from each different language?

• 480

• 450

• 24

• 12

Multiple Choice

8b. A library has 6 English books, 8 French books, and 10 German books. Each book

has a different title. How many ways can you choose:

One book (any language)?

• 480

• 24

• 12

• 240

Multiple Choice

9. How many 5-letter words can be formed from the letters a, b, c, d, e if no letters

are repeated in words?

• 120

• 130

• 140

• 150

Multiple Choice

10. How many 5-letter words can be formed from the letters a, b, c, d, e if

repeated letters are allowed?

• 25

• 125

• 3125

• 225

Multiple Choice

11. How many 5-letter words can be

formed from the letters a, b, c, d, e

starting with a?

• 20

• 24

• 25

• 225

Multiple Choice

12. How many 5-letter words can be

formed from the letters a, b, c, d, e

that do not begin with the letter a?

• 20

• 64

• 96

• 125

Multiple Choice

13. How many words are formed from the word SEMLOHAI?

• P(8,5)

• 8!

• P(8,7)

• C(8,8)

Multiple Choice

14. How many words are formed from the word UNRAM?

• P(6,5)

• P(8,5)

• P(5,5)

• C(5,5)

Multiple Choice

15. How many ways are there if 4 teenagers (w, x, y, z) occupy

the seats that will be arranged in a regular arrangement?

• P(6,3)

• P(7,6)

• P(4,4)

• P(7,5)

Multiple Choice

16. Three exams are conducted in a six-day period (Monday to

Saturday). How many schedule arrangements can be made

so that no two or more exams are conducted on the same

day?

• P(6,3)

• P(7,6)

• P(7,3)

• P(7,5)

Multiple Choice

17. A cinema has rows of seats arranged in rows. Each row

consists of 6 seats. If two people are going to sit, how

many ways are there to arrange the seats in a row?

• P(6,3)

• P(6,2)

• P(6,6)

• P(6,4)

Multiple Choice

18. How many different 2-digit numbers can be arranged

from the numbers 3, 5, and 7?

• 6

• 12

• 18

• 60

Multiple Choice

19. Determine the number of 6-digit numbers arranged from

2 1s, 3 2s, and 1 3!

• 30

• 45

• 60

• 72

Multiple Choice

20. How many permutations of the letters in the word

"JUJUR" are?

• 24

• 30

• 32

• 48

Multiple Choice

21. 100 students are sent to 5 countries, 20 students in each country.

How many ways can students be sent?

• 100!/(20!)

• 100!/(20!)(20!)

• (20!)/(5!)

• 100!/(20!)(20!)(20!)(20!)(20!)

Multiple Choice

22. How many ways can 10 telephones (4 red, 3 white, 3 green, and 2

black) be installed in 12 hotel rooms?

• P(12; 4, 3, 3, 2)

• P(12; 4)

• P(12; 10)

• P(12; 12)

Multiple Choice

23. Four students enter the engineering faculty library. They read at a

round table. How many ways can the four students sit in a circle in

different orders?

• 5

• 4

• 6

• 7

Multiple Choice

24. In a family consisting of a father, a mother, and 3 children eat

together and surround a dining table. How many different ways can

they sit if they move around?

• 20

• 24

• 21

• 36

Multiple Choice

25. 20 apples and 15 oranges are distributed to 5 children, each

child may receive more than 1 apple or orange, or none at

all. How many ways of distribution can be done?

• C(24, 20) x C(19, 15)

• C(20,5) x C(15,5)

• C(25,20) x C(15,5)

• C(25, 20) x C(20, 15)

Multiple Choice

26. From 3 students, namely Budi, Rendi, and Rema, a

badminton doubles pair will be formed. How many doubles

pairs can be formed from the three students?

• 3

• 10

• 12

• 15

Multiple Choice

27. In the preliminary round of a tournament, 25 chess players

compete against each other once. The number of matches

that occur is

• 25

• 30

• 300

• 255