Understanding
In how many ways can the letters of the word LEVEL be arranged if identical letters are considered indistinguishable?
20
Which of the following best defines analogical reasoning?
A. Identifying identical patterns.
B. Solving problems based on numerical logic.
C. Recognizing relationships between pairs of items.
D. Rearranging figures in order.
C. Recognizing relationships between pairs of items.
If P(8, r) = 336, what does this tell you about the number of elements chosen and the importance of order?
A. r = 2, and order matters.
B. r = 3, and order matters.
C. r = 3, and order doesn’t matter.
D. r = 2, and order doesn’t matter.
B. r = 3, and order matters.
4 8 12
6 12 18
8 16 ?
9
Which of the following situations best illustrates a permutation?
A. Choosing 3 students from a group of 10 to receive scholarships.
B. Arranging 3 students in line for class presentation.
C. Forming a 3-member committee from 10 students.
D. Choosing 3 subjects to study from a list of 10.
B. Arranging 3 students in line for class presentation.
How many 4-letter codes can be formed using the first 9 letters of the English alphabet if no letter is repeated?
3024
What number replaces "?"?
8 1 6
3 5 7
4 9 ?
2
Out of 12 students, 3 are to be chosen for officer positions, but their specific roles (President, VP, Secretary) are not assigned yet.
220
What is the main conceptual difference between combination and permutation?
A. Combinations involve repetition.
B. Combinations ignore order, permutations consider order.
C. Permutations ignore order, combinations consider order.
D. Both consider order.
B. Combinations ignore order, permutations consider order.
A license plate consists of 2 letters followed by 3 digits (0–9). If letters and digits can be repeated, how many distinct plates are possible?
676,000
0, 6, 24, 60, ?
120
There are 8 people, including A and B, to be arranged in a circle. In how many ways can they be seated if A and B must sit together?
1,440
A committee of 4 is to be formed from 8 people. If one specific person must always be included, how many possible committees can be formed?
35
From 10 students, 3 are chosen to receive medals (Gold, Silver, Bronze) and will later form a group project team where all have equal roles.
Is this a permutation or a combination?
A. Both permutation
B. Both combination
C. Medal awarding – permutation; project team – combination
D. Medal awarding – combination; project team – permutation
C. Medal awarding – permutation; project team – combination
Why is 0! = 1 important in permutation formulas?
A. It keeps the formula consistent even when r = 0.
B. It simplifies equations in probability.
C. It has no real significance, just convention.
D. It only applies when n = r.
A. It keeps the formula consistent even when r = 0.
In how many ways can 5 students be seated in a row if two specific students must not sit together?
72
If in a certain code, “MATH” is written as “NVUI,” how is “STAT” written?
TUBU
A student notices that each term in the sequence 3, 6, 12, 24, 48, … doubles. If the pattern continues, what will be the ratio of the 7th term to the 5th term?
4
What is the difference between P(n, r) and n!?
A. P(n, r) includes repetitions, n! does not.
B. P(n, r) considers only r objects, while n! uses all n objects.
C. P(n, r) = n! × r!
D. There is no difference.
B. P(n, r) considers only r objects, while n! uses all n objects.
A basketball coach must select 5 players from 12, but 2 players refuse to play together.
672