1. The document contains a mathematics test with 50 multiple choice questions covering topics like permutations, combinations, probability, and sets. 2. It tests concepts like permutations, factorials, combinations formulas, probability calculations, Venn diagrams, dependent and independent events. 3. The questions range from basic computations to word problems involving multiple steps like finding the number of ways to select committee members or the probability of certain events occurring.

1. FELIZARDO C. LIPANA NATIONAL HIGH SCHOOL
THIRD PERIODIC TEST IN MATHEMATICS 10
Direction: Shade the circle O of the letter that correspond to your answer on the answer sheet.
1. It is an arrangement of objects in some specified order.
A. combination B. integration C. differentiation D. permutation
2. Which of the following situations or activities involve permutation?
A. matching shirts and pants B. forming different triangles out of 5 points on a plane, no three of which are collinear
C. assigning telephone numbers to subscribers D. forming a committee from a class
3. Which of the following is the formula to find n objects, taken r at a time?
A.
𝑛!
(𝑛−𝑟)!
B.
𝑛!
(𝑛!−𝑟!)
C.
𝑛!
𝑛!𝑟!
D.
𝑛!
𝑟!(𝑛−𝑟)!
4. The product of a positive integer n and all the positive integers less than it is _____.
A. Powers of n B. n-factors C. Multiples of n D. n-factorial
5. Maine wants a sandwich and a drink for snacks. If a restaurant has 7 choices of sandwiches and 8 choices of drinks. How
many different ways can she order her snacks? A. 15 B. 42 C. 56 D. 72
6. How many total possible outcomes are there for tossing a coin, rolling a six sided number cube and spinning 5 section
spinner? A. 13 B. 60 C. 48 D. 30
7. Compute 5! A. 120 B. 5 040 C. 60 D. 35
8. Simplify
9 !
6!3!
A. 84 B. 28 C. 27 D. 56
9 Which is NOT TRUE about 𝑃 𝑟
𝑛
A. 𝑛 > 𝑟 B. 𝑛 ≥ 𝑟 C. 𝑛 = 𝑟 D. 𝑛 < 𝑟
10. A committee of 5 students is to be chosen from 10 boys and 11 girls. If the committee is all boys, which formula is
applicable? A.
𝑛!
(𝑛−𝑟)!
B.
𝑛!
(𝑛!−𝑟!)
C.
𝑛!
𝑛!𝑟!
D.
𝑛!
(𝑛−𝑟)!𝑟!
11. In how many ways can a president, vice- president, secretary and treasurer be chosen from a club with 8 members?
A. 840 B. 1 320 C. 132 D. 1680
12. Which of the following expressions represents the number of distinguishable permutations of the letters of the word
CONCLUSIONS? A. 11! B.
11!
8!
C.
11!
2!2!2!
D.
11!
2!2!2!2!
13. In how many ways can 8 people be seated around a circular table if two of them insist on sitting beside each other?
A. 360 B. 720 C. 1440 D. 5040
14. If P ( 9, r) = 504. What is r? A. 7 B. 6 C. 5 D. 3
15. If P(n, 3) = 60, then n=_____ A. 6 B. 9 C. 10 D. 5
16. Given x = P ( n, n) and y = P (n, n-1) What can be concluded about x and y? A. 𝑥 > 𝑦 B. 𝑥 < 𝑦 C. x = y D. x = -y
17. C ( n, n) = ________ A. n B. r C. 1 D. cannot be determined
18. If C ( n, r) = 35, which of the following are possible values of n and r?
A. n = 6 r = 4 B. n = 7 r = 3 C. n = 8 r = 3 D. n = 9 r = 2
19. Joel was assigned by his teacher to get the number of ways can 4 members of a committee be selected in 8 aspirants , but
he already forgot the steps on how to solve it, let us help him to do this by listing out the procedure.
I. Required: State what is asked in the problem.
II. Analysis : Analyze whether the given problem is an example of permutation of combination
III. Given: Identify the value of n and r
IV. Formula: Identify the appropriate formula.
V. Solve. Solve the problem using 𝐶(𝑛, 𝑟) =
𝑛!
(𝑛−𝑟)!𝑟!
A. II, I, V, IV, III B. II, I, III, IV, V C. I, II, III, IV, V D. III, V, IV, I, II
20. When you roll a die, which of the following is the sample space?
A. S = {1, 2, 3, 4, 6} C. S = {2, 4, 6}
B. S = {1, 2, 3, 4, 5, 6} D. S = {3, 4, 5, 6}
21. What statement does the shaded region of the figure at the right represent?
A. C or D B. C C. C and D D. D
22. What statement does the shaded region of the figure at the right represent?
A. A or B C. Not A
B. A and B D. Not B

2. Use the figure on the left to answer numbers 23 and 24.
23. What event set represents the union of the sets A and B?
A. {2, 4, 8} B. {5, 6, 7, 9, 12} C. {6, 12} D. {2, 4, 5, 6, 7, 8, 9, 12}
24. What event set represents the intersection of the sets A and B?
A. {2, 4, 8} B. {5, 6, 7, 9, 12} C. {6, 12} D. {2, 4, 6, 8, 12}
25. Measure of how likely an event is to occur is called ________
A. permutation B. combination C. probability D. distinction
26. Which of the following probability cannot exist?
A.
2
5
B. 1 C. 0 D. -
1
2
27. Which event is certain to happen?
A. A boy is getting pregnant B. Rolling a die and getting 2
C. Philippines will experience snow D. Drawing 11 from an ordinary deck of cards
28. Which of the following are the outcomes in tossing a single coin?
A. head or tail B. S = {head, tail} C. a head D. a tail
29. What does this symbol “∪” represents?
A. intersection, “and” B. union, “and” C. intersection, “or” D. union, “or”
30. A coin is tossed three times. The probability of getting three heads is
1
8
, what is the cardinality of the sample space?
A. 1 B. 8 C. 6 D. 2
31. What is the probability of getting a tail when tossing a coin once?
A.
1
2
B.
1
4
C.
1
3
D.
2
5
32. In a deck of card, what is the probability of getting a king or queen?
A. 2/13 B. 3/13 C. 4/13 D. 5/13
33. If (5) means that there are 5 elements in the set P ∩ Q, how many elements are there in P ∪ Q?
A. 22 B. 23 C. 24 D. 25
34. Referring to number 33, how many elements does P have?
A. 11 B. 13 C. 14 D. 15
35. Referring to number 33, how many elements does Q have?
A. 11 B. 13 C. 14 D. 15
36. Referring to number 33, how many elements does (PUQ)’.
A. 2 B. 3 C. 4 D. 5
37. Brian likes to wear colored shirts. He has 10 shirts in the closet. Three of these are blue, four are in different shades of
red, and the rest are of mixed or different colors. What is the probability that he will wear a blue or a red shirt?
A. 7/10 + 4/10 B. 3/10 + 4/10 C. 3/10 + 7/10 D. 7/10 - 4/10
38. The spinner on the right is spun. What is the probability of a spin that results in an even
number or a number less than 4?
A. 1/4
B. 3/4
C. 4/8
D. 5/8
39. A nationwide survey revealed that 42% of the population likes eating pizza. If two people are randomly selected from the
population, what is the probability that the first person likes eating pizza and the second one does not?
A. 0.42 + (1 − 0.42) B. 1 - 0.42 C. (2) (1 − 0.42) D. (0.42) (1 − 0.42)
40. The events A and B are mutually exclusive. Which of the following is true about the probability of A or B?
A. P(A ∪ B) = P(A) + P(B) B. P(A∪ B) = P(A) – P(B)
C. P(A∪ B) = P(A) + P(B) – P(A ∩B) D. P(A∪ B) = P(A) – P(B) + P(A ∩ B)
41 Which of the following diagrams illustrate mutually exclusive events?
A. B. C. D.

3. 42. Which of the following situations illustrate mutually exclusive event?
A. Turning left and turning right
B. Turning left and scratching your head
C. Drawing kings and hearts in a standard deck of cards
D. Getting an odd and a number less than 3 when rolling a die?
43. Which of the following pairs is a not-mutually exclusive events?
I. Sit down and stand up
II. Dance and pinch your nose
III. Two dice: Odd and even
IV.Getting a head and a tail when tossing a coin
A. II only B. III only C. II and III only D. All of the above
44. The probability that a visit to the school clinic is neither due to dental reasons nor medical reasons is 35%. Of those coming
to the clinic, 30% are due to medical reasons and 40% are due to dental reasons. What is the probability that a visit to the school
clinic is due to both dental and medical reasons?
A. 0.05 B. 0.12 C. 0.18 D. 0.25
45. A diagram that uses circles to represents sets, in which the relations between the sets are indicated by the arrangement of
the circles. A. Venn Diagram B. tree diagram C. pie chart D. bar graph
46. ERROR ANALYSIS. George and Aliyah are determining the probability of randomly choosing a blue or red marble from
a bag of 8 blue marbles, 6 red marbles, 8 yellow marbles and 4 white marbles. Which of them is correct? Explain.
A. Aliyah, to find the probability of blue or red, the individual probabilities should be added because the
events are mutually exclusive.
B. Aliyah, to find the probability of blue or red, the individual probabilities should be added because the events are not
mutually exclusive.
C. George, to find the probability of blue or red, the individual probabilities should be multiply because the
events are dependent.
D. George, to find the probability of blue or red, the individual probabilities should be multiply because the
events are independent.
For numbers 47-48, use the data given below. A sample of 150 plastic pipes were selected and subjected to shock
resistance and scratch resistance tests. The results are summarized in the table below.
47. How many plastic pipes are high shock resistance?
A. 125 B. 132 C. 137 D. 12
48. What is the probability that it has high scratch resistance and high shock resistance?
A.
125
150
B.
125
137
C.
137
150
D.
132
150
49. The events A and B are dependent. Which of the following is true about the probability of A and B?
A. P(A ∩ B) = P(A) ∙ P(B) B. P(A∩ B) = P(A) ∙ P(B/A)
C. P(A∪ B) = P(A) + P(B) – P(A ∩B) D. P(A∪ B) = P(A) – P(B) + P(A ∩ B)
50. A flashlight has 6 batteries, 2 of which are defective. If 2 are selected at random without replacement, find the probability
that both are defective.
A.
1
28
B.
2
3
C.
1
15
D.
1
16
Prepared by:
JOSEPHINE M. VALENCIA
MARICEL P. ABLAZA
GEORGE
𝑃(𝑏𝑙𝑢𝑒 ∪ 𝑟𝑒𝑑 = 𝑃(𝑏𝑙𝑢𝑒) ∙ 𝑃(𝑟𝑒𝑑)
=
8
26
∙
6
26
=
48
676
about 7%
ALIYAH
𝑃(𝑏𝑙𝑢𝑒 ∪ 𝑟𝑒𝑑 = 𝑃(𝑏𝑙𝑢𝑒) + 𝑃(𝑟𝑒𝑑)
=
8
26
+
6
26
=
14
26
about 54%

4. 1. D
2. C
3. A
4. D
5. C
6. B
7. A
8. A
9. D
10. D
11. D
12. D
13. B
14. D
15. D
16. C
17. C
18. B
19. B
20. B
21. A
22. B
23. D
24. C
25. C
26. D
27. B
28. B
29. D
30. B
31. A
32. A
33. A
34. B
35. C
36. A
37. B
38. B
39. D
40. A
41. C
42. A
43. C
44. A
45. A
46. A
47. B
48. A
49. A
50. C
KEY TO CORRECTION