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Q 1/50
Score 0
A school offers 4 music clubs and 3 sports clubs. A student may join only one cluWhich counting principle should be used to determine the total number of possible choices?
60
Multiplication Principle
Combination Principle
Addition Principle
Permutation Principle
Q 2/50
Score 0
A cafeteria allows students to choose one main dish and one drink. Which counting principle is appropriate for finding the total number of meal choices?
60
Combination Principle
Permutation Principle
Multiplication Principle
Addition Principle
50 questions
Q.
A school offers 4 music clubs and 3 sports clubs. A student may join only one cluWhich counting principle should be used to determine the total number of possible choices?
1
60 sec
Q.
A cafeteria allows students to choose one main dish and one drink. Which counting principle is appropriate for finding the total number of meal choices?
2
60 sec
Q.
Which situation illustrates the Addition Principle?
3
60 sec
Q.
A science teacher asks students to either:
A: arrange the top three winners in a quiz contest, or
B: select three students to represent the class in a seminar.
Which statement correctly identifies the counting methods?
4
60 sec
Q.
Four classmates discuss whether a situation involves permutations or combinations.
Ana: Order matters.
Ben: Objects are only selected.
Cara: Positions are assigned.
Dan: Ranking is important.
Which students are describing permutations?
5
60 sec
Q.
A school event includes the following activities:
I. Electing a president, vice president, and secretary
II. Choosing five volunteers for a clean-up drive
III. Awarding gold, silver, and bronze medals
Which activities require permutations?
6
60 sec
Q.
A class has 8 students competing for President, Vice President, and Secretary. How many different ways can these officers be chosen?
7
60 sec
Q.
A basketball coach must choose 5 players from 10 team members to start the game. How many different starting lineups are possible?
8
60 sec
Q.
A company has 7 qualified employees. Three different leadership positions must be assigned. How many assignments are possible?
9
60 sec
Q.
A teacher wants to select 4 students from a class of 9 to participate in a Math OlympiaHow many different groups can be formed?
10
60 sec
Q.
A student claims that 10C3​ and 10C7​ always have the same value. Which explanation best justifies the claim?
11
60 sec
Q.
Which statement best explains why 12C5 = 12C7​?
12
60 sec
Q.
A teacher asks students to determine whether it is easier to compute 15C13​ directly or use a property of combinations. Which reasoning is most appropriate?
13
60 sec
Q.
A student solved the following problem:
"How many ways can a president, vice president, and secretary be selected from 8 students?"
The student used the solution: 8C3 = 56
How would you evaluate the student's solution?
14
60 sec
Q.
Two students solved the same problem:
"Choose four members from ten students to represent the class."
Student A: 10C4 = 210
Student B: 10P4 = 5040
Which student's solution should be accepted?
15
60 sec
Q.
A teacher asks students to solve the following:
"Award gold, silver, and bronze medals to 12 finalists."
Which method is the best choice?
16
60 sec
Q.
How many distinct arrangements can be formed using the letters of the word BALLOON?
17
60 sec
Q.
Six friends are seated around a circular table. How many different seating arrangements are possible?
18
60 sec
Q.
A family wants to arrange the letters of the word LEVEL for a decorative banner. How many distinct arrangements are possible?
19
60 sec
Q.
Eight different books are to be distributed equally among two students, with each student receiving four books. How many different distributions are possible?
20
60 sec
Q.
Five identical gift bags are to be distributed among three children. Which statement correctly describes this problem?
21
60 sec
Q.
Three different prizes are to be given to three different winners from a group of eight students. Which counting technique is most appropriate?
22
60 sec
Q.
A student must choose one Mathematics elective from 4 options and one Science elective from 3 options. How many different schedules are possible?
23
60 sec
Q.
A password consists of two different letters followed by one digit. There are 26 letters and 10 digits available. How many passwords are possible?
24
60 sec
Q.
A school plans to form a committee consisting of 1 chairperson, 1 vice-chairperson, and 4 members from 12 teachers. Which sequence of counting techniques is most appropriate?
25
60 sec
Q.
A die is rolled once.
Sample Space: S = {1, 2, 3, 4, 5, 6}
Event A = "an even number"
Which correctly lists Event A?
26
60 sec
Q.
A card is drawn from cards numbered 1–10. Event B = "drawing a number greater than 6." Which set correctly represents Event B?
27
60 sec
Q.
A spinner has sections labeled:
Red, Blue, Green, Yellow
Event C = "landing on a warm color."
Which correctly represents Event C?
28
60 sec
Q.
A bag contains balls labeled: A, B, C, D, E
Event D = "drawing a vowel."
Which represents Event D?
29
60 sec
Q.
A student claims that the probability of drawing a king from a standard deck of cards is 1/13​. How would you evaluate the student's answer?
30
60 sec
Q.
Two students solved the same problem.
"A bag contains 3 red, 2 blue, and 5 green marbles. Find the probability of drawing a blue marble."
Student A: 2/10
Student B: 2/5
Which solution is correct?
31
60 sec
Q.
A teacher solved a probability problem using permutations when selecting three committee members from ten students. How should this solution be evaluated?
32
60 sec
Q.
A class consists of 12 boys and 18 girls. A student says,
"The probability of choosing a girl is 18/12."
What is the best evaluation?
33
60 sec
Q.
When rolling one die, consider the events:
A = getting an even number
B = getting an odd number. Which statement is true?
34
60 sec
Q.
A card is drawn.
Event A = drawing a queen
Event B = drawing a heart
Are these events mutually exclusive?
35
60 sec
Q.
A spinner has numbers 1–8.
Event A = landing on a multiple of 2
Event B = landing on a multiple of 4
These events are
36
60 sec
Q.
A bag contains 7 white balls and 3 black balls.
A student says the probability of not drawing a white ball is 1− (7/10)
How should this solution be evaluated?
37
60 sec
Q.
In a class,
18 students play basketball,
15 play volleyball,
5 play both.
A student computes 18 + 15 = 33
Which evaluation is correct?
Which student's reasoning correctly explains why the overlap is subtracted when finding P(A∪B)?
40
60 sec
Q.
Which situation involves conditional probability?
41
60 sec
Q.
A teacher asks: "What is the probability that a student is left-handed given that the student plays basketball?" This is
42
60 sec
Q.
Which characteristic distinguishes conditional probability from simple probability?
43
60 sec
Q.
A box contains 5 red and 3 blue balls.
One red ball is drawn and not replaced.
A student claims the probability that the second ball is blue is 3/8. How should the solution be evaluated?
44
60 sec
Q.
A class has 20 students. 12 are girls. 8 girls wear glasses. Find P(Glasses ∣ Girl)
45
60 sec
Q.
A student solved a conditional probability problem by using the original sample space even after one card had already been removed. What error did the student make?
46
60 sec
Q.
Two cards are drawn without replacement. Which expression correctly represents the probability that both cards are kings?
47
60 sec
Q.
Which pair of events is independent?
48
60 sec
Q.
A teacher says, "If the occurrence of Event A changes the probability of Event B, then the events are independent." How should this statement be analyzed?
