Question 1

The arrangement of n objects in a specific order is referred to:

Accepted Answer

permutation

Answer

combination

Answer

probability

Answer

factorial

Question 2

Which of the following methods rearranges objects by means of showing them systematically through a diagram?

Accepted Answer

tree diagram

Answer

graphical method

Answer

listing method

Answer

tabular method

Question 3

Which of the equations below illustrates the number of permutations of n objects taken r at a time?

Accepted Answer

P(n,r) = n(n-1)(n-2)...(n-r+1)

Answer

P(n,r) = n(n-1)

Answer

P(n,r) = n(n-1)(n-s)!

Answer

P(n,r) = n!

Question 4

In the permutation of n objects taken r at a time, which of the following is true?

Accepted Answer

n ≥ r

Answer

n < r

Answer

n > r

Answer

n ≤ r

Question 5

The different ways in which the letters R, S, T can be grouped together taken all at a time are RST, RTS, STR, TSR, TRS, SRT. Which method of arrangement is illustrated?

Accepted Answer

listing method

Answer

tree diagram

Answer

graphical method

Answer

tabular method

Question 6

In the problem: How many ways can a student select a president, vice-president, secretary, and treasurer from a group of 5 people?", what are the values of n and r, respectively?

Accepted Answer

5 and 4

Answer

5 and 6

Answer

6 and 5

Answer

4 and 5

Question 7

Which of the following listing shows a combination?

Accepted Answer

LMN, LMO, LNO, MON

Answer

56, 65, 48, 84

Answer

123, 231, 321, 213

Answer

AB, BA, CA, AC

Question 8

Which is true about combination?

Accepted Answer

order is not important

Answer

same as permutation

Answer

sequence of objects

Answer

arrangement of objects matters

Question 9

What is the expanded form of ₈C₃?

Accepted Answer

$C\left(8,3\right)\ =\ \frac{8!}{3!\left(8-3\right)!}$

Answer

$C\left(8,3\right)\ =\ \frac{8!}{3!\left(8-3\right)!}$

Answer

$C\left(8,3\right)\ =\ \frac{8!}{3!\left(8-3\right)!}$

Answer

$C\left(8,3\right)\ =\ \frac{8!}{3!\left(8-3\right)!}$

Question 10

Which of the following is an example of combination?

Accepted Answer

selecting three team members from the group

Answer

arranging people

Answer

electing a president and vice-president in an organization

Answer

selecting first, second and third place winners

Question 11

Which of the following situations shows that order is NOT important?

Accepted Answer

buying 5 out of 9 designs of facemask

Answer

assembling jigsaw puzzle

Answer

setting a 6-digit code in a vault

Answer

selecting top 4 winners in Math Quiz

Question 12

What is the keyword that best describes a combination from the given problem? A bookstore has 7 types of notebooks wherein you need to buy 3. how many different selections can you make if repetition is allowed?

Accepted Answer

selections

Answer

7 types of notebooks

Answer

repetition

Answer

3 out of 7

Question 13

It refers to the set of all possible outcomes of a probability experiment.

Accepted Answer

sample space

Answer

event

Answer

probability

Answer

outcomes

Question 14

if events consist of more than one outcome, the events are likely to be ________.

Accepted Answer

compound events

Answer

complement events

Answer

mutually exclusive events

Answer

simple events

Question 15

It consists of all outcomes that are both in events A and B, denoted by A $\cap$ B.

Accepted Answer

Intersection of events

Answer

simple events

Answer

compound events

Answer

union of events

Question 16

The following are compound events EXCEPT

Accepted Answer

drawing a red ball from a box with 3 red balls, 5 yellow balls and 2 blue balls

Answer

getting a 1 and a 6 when 3 dice are rolled

Answer

taking out a number 5 or a number divisible by 3 from a bowl containing chips number 1 to 15

Answer

choosing a milk chocolate and then a white chocolate from a box of assorted chocolates

Question 17

If a set contains all the elements that are in both events A or B, then it likely implies that:

Accepted Answer

There is union between events A and B

Answer

An intersection takes place between A and B

Answer

Events A and B are independent to each other

Answer

Event A is dependent to event B

Question 18

If an event is in set R but not in set S, which of the following statements is true?

Accepted Answer

The event is in the union of R and S

Answer

The event is in both the union and intersection of R and S

Answer

The event is not in the union of R and S

Answer

The event is in the intersection of R and S

Question 19

If there is/are outcome (s) found in both the two events A and B, which of the following describes the general rule in finding the probability of A or B?

Accepted Answer

P (A $\cap$ B) = P(A) +P(B) - P(A $\cap$ B)

Answer

P (A $\cap$ B) = P(A) +P(B) + P(A $\cap$ B)

Answer

P (A $\cap$ B) = P(A) - P(B) - P(A $\cap$ B)

Answer

P (A $\cap$ B) = P(A) +P(B) - P(A $\cap$ B)

Question 20

When there are no common outcomes in P(A) and P(B), which equation will determine the P(AUB)?

Accepted Answer

P (A $\cap$ B) = P(A) - P(B)

Answer

P (A $\cap$ B) = P(A) + P(B)

Answer

P (A $\cap$ B) = P(A) +P(B) - P(A $\cap$ B)

Answer

P (A $\cap$ B) = P(A) - P(B) + P(A $\cap$ B)

Question 21

It is the set of all outcomes that are not in the event A, denoted by A'.

Accepted Answer

complement of an event

Answer

compound events

Answer

union of events

Answer

intersection of events

Question 22

The probability of heads landing up when you flip a coin is 1/2. What is the probability of getting tails if you flip it again?

Accepted Answer

1/2

Answer

1/4

Answer

1/3

Answer

3/4

Question 23

A survey revealed that 47% of the population liked eating hamburgers. If two people are randomly selected from the population, what is the probability that the first person likes eating hamburger while the second does not?

Accepted Answer

0.47 (1 - 0.47)

Answer

1 - 0.47

Answer

0.47 $\cap$ (1 - 0.47)

Answer

2 (1 - 0.47)

Question 24

A day of the week is selected at random. What is the probability that it is Saturday?

Accepted Answer

1/7

Answer

2/7

Answer

1

Answer

6/7

Question 25

In finding the probability that either A or B occurs, what formula is best to use when the two events are mutually exclusive?

Accepted Answer

P (A or B) = P(A) + P(B)

Answer

P (A or B) = P(A) - P(B)

Answer

P (A or B) = P(A) + P(B) - P(A and B)

Answer

P (A or B) = P(A) - P(B) + P(A and B)

Question 26

Which of the following exemplifies a mutually exclusive event?

Accepted Answer

going up and down the elevator

Answer

driving and listening to radio

Answer

drawing an ace and a spade in a standard deck of 52 cards

Answer

running and sweating

Question 27

Which among the conditions below justifies that an event is non-mutually exclusive?

Accepted Answer

two or more events may occur at the same time

Answer

the probability of two or more events at the same time is zero

Answer

the events cannot happen if another related event happens

Answer

two or more events have no outcomes in common

Question 28

Suppose an ordinary die is rolled, what equation will help you determine the probability of getting an event number or a number divisible by 3?

Accepted Answer

P (A U B) = 3/6 + 2/6 - 1/6

Answer

P (A U B) = 3 - 2 - 1

Answer

P (A U B) = 2/6 + 1/2 + 6

Answer

P (A U B) = 1/2 - 1/3 - 1/6

Question 29

If P(A) = 1/3, P(B) = 1/2 and P(A U B) = 5/6, then events A and B are:

Accepted Answer

mutually exclusive events

Answer

dependent events

Answer

non-mutually exclusive events

Answer

independent events

Question 30

What is the value of P (A $\cap$ B) if A = {1, 2, 3, 4, 5}, and B = {2, 4, 6, 8, 10}?

Accepted Answer

1/4

Answer

1/2

Answer

1/5

Answer

3/10

Question 31

What is the permutation of 10 objects taken 3 at a time?

Accepted Answer

720

Answer

3, 628, 800

Answer

10

Answer

30

Question 32

Consider the problem: How many different ways can 5 books be arranged on a shelf if they can be selected from 7 books?

Accepted Answer

P (7,5) = 7 x 6 x 5 x 4 x 3

Answer

P (5,7) = 5 x 6 x 7 x 8 x 9 x 10 x 11

Answer

P (5,5) = 5!

Answer

P (7,7) = 7!

Question 33

A girl was invited to a party. She has several available blouses and skirts on her closet. Knowing that any of her blouses can be paired with any of her skirts, she calculated that she could have 42 blouse-skirt pairing to choose to. Which of the following could be the number of blouses and skirts the girls has in her closet?

Accepted Answer

7 blouses, 6 skirts

Answer

6 blouses, 7 skirts

Answer

7 blouses, 7 skirts

Answer

6 blouses, 6 skirts

Question 34

Numbers with the same number of digits shall be formed from 2, 4, 5, 7, 8, and 9 such that repetition of digit is not allowed. If 720 numbers can be formed, how many digits do these numbers contain?

Accepted Answer

4

Answer

6

Answer

3

Answer

5

Question 35

Anna, dress-shop owner has several new dresses to be displayed through her available mannequins. If she can dress these mannequins in 60 different ways, which of the following could be the number of new dresses and mannequins she has?

Accepted Answer

5 new dresses, 3 mannequins

Answer

3 new dresses, 4 mannequins

Answer

5 new dresses, 4 mannequins

Answer

3 new dresses, 3 mannequins

Question 36

The number of permutations of the 4-letter word HOPE taken 2 as a time is 12, find its number of combinations.

Accepted Answer

6

Answer

4

Answer

2

Answer

8

Question 37

From the situation given, determine if the scenario involves permutation or combination, then find the number of possibilities. "There are 9 applicants for three Computer Programmer positions."

Accepted Answer

combination; 84

Answer

permutation; 3 024

Answer

combination; 504

Answer

permutation; 504

Question 38

How does combination differ from permutation?

Accepted Answer

order of the objects

Answer

counting of sets

Answer

grouping of objects

Answer

arrangement of things

Question 39

What ideas apply in the combination that cannot be applied in the permutation?

I. Different ways of arranging set of objects

II. Insignificant order

III. Selecting items from a large set of objects

IV. Ordered elements

Accepted Answer

II, III

Answer

II, IV

Answer

II, III, IV

Answer

I, II, III, IV

Question 40

If w = C(5,2), x = C(5,3), y = C(5,4), and z = C(5,5), and we are given 5 points on a plane of which no three are collinear, which expression gives the total number of polygons that can be drawn?

Accepted Answer

x + y + z

Answer

x + y

Answer

w +x + y

Answer

w + x + y + z

Question 41

There are 11 different food items in a buffet. A costumer is asked to get a certain number of items. If the customer has 462 possible ways as a result, which of the following did he possibly do?

Accepted Answer

choose 6 out of the 11 items

Answer

choose 4 out of the 11 items

Answer

choose 7 out of the 11 items

Answer

choose 8 out of the 11 items

Question 42

Samantha is transferring to a new house. She has a collection of books but she cannot take them all with her. In how many ways can she select 7 books out of 10, and then arrange these books on a shelf if there is space enough for only 5 books?

Accepted Answer

302 400

Answer

3 024

Answer

3 024 000

Answer

30 240

Question 43

In how many ways can a committee of 5 be formed from 5 juniors and 7 seniors if the committee must have 3 seniors?

Accepted Answer

350

Answer

520

Answer

720

Answer

240

Question 44

If a combination lock must contain 5 different digits, in how many ways can a code be formed from the digits 0 to 9?

Accepted Answer

30 240

Answer

151 200

Answer

1 000 000

Answer

15 120

Question 45

A card is drawn at random from a well-shuffled deck of cards. Find the probability that the card is a face card or an ace?

Accepted Answer

4/13

Answer

1/4

Answer

13/52

Answer

1/13

Question 46

If P(A) = 17/50, P(B) = 11/25, and P (A $\cap$ B) = 2/25, what is P(A U B)?

Accepted Answer

70%

Answer

30%

Answer

62%

Answer

78%

Question 47

A veterinarian surveys his patrons about the kind of pets they have at home. He revealed the following information:

i. 53% have dogs

ii. 38% have cats

iii. 19% have fish

iv. 15% have dogs and cats

v. 12% have dogs and fish

vi. 4% have cats and fish

If no one has all three kinds of pets, what is the probability that patrons have none of these pets?

Accepted Answer

21%

Answer

17%

Answer

26%

Answer

13%

Question 48

The grade 10 class has 40 students who took two examinations in mathematics. 26 students passed the first examination and 30 passed the second. If 8 students failed both exams, what is the probability that students passed the two exams?

Accepted Answer

3/5

Answer

3/20

Answer

9/10

Answer

17/20

Question 49

A group of 30 tourists are planning for a tour at the three renowned tourist destinations of Surigao del Sur. 16 wants to visit Enchanted River, 16 chooses Britania Islands, and 11 to Tinuy-an Falls. 5 says they want to take both Enchanted River and Tinuy-an Falls, and of these, 3 wanted to visit Britania Islands as well. 5 wants only Tinuy-an Falls, and 8 wants only Britania Islands.

Suppose event A refers to tourist visiting Enchanted River and event B refers to tourists visiting Britania Islands. How can you show the probability that a tourist visits either A or B?

Accepted Answer

7/10

Answer

17/30

Answer

12/30

Answer

16/30

Question 50

A group of 30 tourists are planning for a tour at the three renowned tourist destinations of Surigao del Sur. 16 wants to visit Enchanted River, 16 chooses Britania Islands, and 11 to Tinuy-an Falls. 5 says they want to take both Enchanted River and Tinuy-an Falls, and of these, 3 wanted to visit Britania Islands as well. 5 wants only Tinuy-an Falls, and 8 wants only Britania Islands.

Suppose event A refers to tourist visiting Enchanted River and event B refers to tourists visiting Britania Islands. How can you show the probability that a tourist visits either A or B?

Accepted Answer

P (A U B) = 8/15 + 8/15 - 7/30

Answer

P (A U B) = 8/15 + 11/30 - 1/6

Answer

P (A U B) = 11/30 - 8/15 + 2/15

Answer

P (A U B) = 16/30 + 11/30 - 7/30

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