Podcast
Questions and Answers
What is the key difference between permutation and combination?
What is the key difference between permutation and combination?
- Permutation considers order, combination does not (correct)
- Combination involves probability, permutation does not
- Combination deals with arrangement, permutation with selection
- Order is important in both
How many ways can Sir Jayson choose 6 individuals from the 15 players who applied for the team?
How many ways can Sir Jayson choose 6 individuals from the 15 players who applied for the team?
- 5, 005 (correct)
- 12, 376
- 8, 910, 700
- 3, 603, 600
What is the correct description of the intersection of events in drawing cards?
What is the correct description of the intersection of events in drawing cards?
- Drawing a face card and a red card (correct)
- Drawing a face card and a club card
- Drawing a face card or a king card
- Drawing a king card or a diamond card
What does the shaded portion in the figure represent?
What does the shaded portion in the figure represent?
What is the key difference between permutation and arrangement?
What is the key difference between permutation and arrangement?
If 17 players applied for the team, how many ways can Sir Jayson choose 6 individuals?
If 17 players applied for the team, how many ways can Sir Jayson choose 6 individuals?
What is the correct statement about the relationship between permutation and combination?
What is the correct statement about the relationship between permutation and combination?
What does the union of events represent in drawing cards?
What does the union of events represent in drawing cards?
What is the sample space in the context of drawing cards?
What is the sample space in the context of drawing cards?
What is the correct description of the complement of events in drawing cards?
What is the correct description of the complement of events in drawing cards?
Flashcards
Permutation vs. Combination
Permutation vs. Combination
Permutation considers the order of items, while combination does not consider order.
Choosing individuals (15 from 6)
Choosing individuals (15 from 6)
The number of ways to choose 6 individuals from 15 players is 5,005.
Intersection of Events (Cards)
Intersection of Events (Cards)
The intersection of events involves outcomes that satisfy both events. E.g., Drawing a card that is both a face card and red.
Relationship: Permutation & Combination
Relationship: Permutation & Combination
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Union of events (cards)
Union of events (cards)
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Sample Space
Sample Space
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Complement of Events (Cards)
Complement of Events (Cards)
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Study Notes
Mathematics Review for Grade 10
Sequences and Series
- Identify the next number in the sequence 7, 15, 24, 34, ___: A. 43, B. 44, C. 45, D. 46
- Formula for permutation of non-distinct objects: P(n, r) = n! / (n-r)!
- Arithmetic mean of 3 and 15: A. 10, B. 9
Probability
- Sample space: all possible outcomes of an experiment
- Event: a set of outcomes of an experiment
- Probability of an event: number of favorable outcomes / total number of possible outcomes
Circles
- Center and radius of a circle: C (0, 0); r = 4, or C (1, 1); r = 4
- Equation of a circle: (x - 5)² + (y - 0)² = 25
- Area of a circle: πr²
Combinatorics
- Permutation: arrangement of objects in a specific order
- Combination: selection of objects without regard to order
- Formula for permutation: P(n, r) = n! / (n-r)!
- Formula for combination: C(n, r) = n! / (r!(n-r)!)
- Example: number of ways to choose 6 individuals from 15 players: A. 5, 005, B. 12, 376, C. 3, 603, 600, D. 8, 910, 700
Polynomials
- Factoring polynomials: finding the linear factors of a quadratic expression
- Example: x² + 5x - 6 = (x + 6)(x - 1)
Geometry
- Semicircle arch: diameter = 4 meters, length of iron before bending = π meters
- Circle inside a square: radius = 4 inches, area = 16Ï€ sq.in.
Sets
- Union of sets: all elements in either set A or set B
- Intersection of sets: all elements common to both sets A and B
- Example: A = {1, 2, 3, 4}, B = {4, 5, 6, 7}, A ∪ B = {1, 2, 3, 4, 5, 6, 7}, A ∩ B = {4}
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