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Questions and Answers
A club with 6 members needs to elect a president, vice president, and secretary. In how many ways can these positions be filled, assuming no one can hold more than one position?
A club with 6 members needs to elect a president, vice president, and secretary. In how many ways can these positions be filled, assuming no one can hold more than one position?
- 216
- 20
- 720
- 120 (correct)
A committee of 4 students is to be formed from a group of 10 students. How many different committees can be formed?
A committee of 4 students is to be formed from a group of 10 students. How many different committees can be formed?
- 210 (correct)
- 10000
- 40
- 5040
What is the fundamental difference between a permutation and a combination?
What is the fundamental difference between a permutation and a combination?
- Permutations consider the order of items, while combinations do not. (correct)
- Permutations involve selections from a smaller set, while combinations involve selections from a larger set.
- Permutations are used for mutually exclusive events, while combinations are used for independent events.
- Permutations calculate probabilities, while combinations calculate averages.
A bag contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that both are red?
A bag contains 5 red balls and 3 blue balls. If two balls are drawn at random, what is the probability that both are red?
What is the probability of rolling a sum of 7 or 11 with two dice?
What is the probability of rolling a sum of 7 or 11 with two dice?
Event A and Event B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is P(A or B)?
Event A and Event B are mutually exclusive. If P(A) = 0.3 and P(B) = 0.4, what is P(A or B)?
Two events are independent. The probability of event A occurring is 1/2. The probability of event B occuring is 4/52. What is the probability of both events occuring?
Two events are independent. The probability of event A occurring is 1/2. The probability of event B occuring is 4/52. What is the probability of both events occuring?
What does it mean for two events to be mutually exclusive?
What does it mean for two events to be mutually exclusive?
A coin is tossed and a die is rolled. What is the probability of getting a tail on the coin and a 4 on the die?
A coin is tossed and a die is rolled. What is the probability of getting a tail on the coin and a 4 on the die?
What formula is used when two events are mutually exclusive to determine the probability of either event occurring?
What formula is used when two events are mutually exclusive to determine the probability of either event occurring?
Find the distance between points A(2, 3) and B(5, 7).
Find the distance between points A(2, 3) and B(5, 7).
What is the midpoint between the points (1, 5) and (7, -1)?
What is the midpoint between the points (1, 5) and (7, -1)?
What is the standard form equation of a circle with center (h, k) and radius r?
What is the standard form equation of a circle with center (h, k) and radius r?
What is the general form of the equation of a circle?
What is the general form of the equation of a circle?
Given the equation of a circle $(x - 3)^2 + (y + 2)^2 = 25$, what is the center and radius of the circle?
Given the equation of a circle $(x - 3)^2 + (y + 2)^2 = 25$, what is the center and radius of the circle?
Transform the circle equation $(x - 2)^2 + (y + 3)^2 = 9$ into general form.
Transform the circle equation $(x - 2)^2 + (y + 3)^2 = 9$ into general form.
You have 5 different books to arrange on a shelf. How many different arrangements are possible if the order of the books matters?
You have 5 different books to arrange on a shelf. How many different arrangements are possible if the order of the books matters?
In a game, the probability of winning is 0.6. If you play the game twice, what is the probability of winning both times, assuming the games are independent?
In a game, the probability of winning is 0.6. If you play the game twice, what is the probability of winning both times, assuming the games are independent?
A bag contains 7 green marbles and 3 yellow marbles. What is the probability of randomly selecting a green marble, not replacing it, and then selecting another green marble?
A bag contains 7 green marbles and 3 yellow marbles. What is the probability of randomly selecting a green marble, not replacing it, and then selecting another green marble?
Calculate the midpoint of a line segment with endpoints at coordinates (1,2) and (5, 8).
Calculate the midpoint of a line segment with endpoints at coordinates (1,2) and (5, 8).
Flashcards
Permutations
Permutations
Arrangements where order matters.
Combinations
Combinations
Selections where order doesn't matter.
N (in Combinations formula)
N (in Combinations formula)
The number of total objects in the set.
R (in Combinations formula)
R (in Combinations formula)
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Probability
Probability
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Experiment
Experiment
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Outcomes
Outcomes
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Sample space
Sample space
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Event (in probability)
Event (in probability)
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Compound event
Compound event
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Probability of zero
Probability of zero
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Probability of 1
Probability of 1
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Mutually Exclusive
Mutually Exclusive
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Independent Events
Independent Events
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Midpoint
Midpoint
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Distance Formula
Distance Formula
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x² + y² + ax + by + c = 0
x² + y² + ax + by + c = 0
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(h,k)
(h,k)
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Study Notes
Permutation vs Combination
- Permutations are arrangements where the order matters.
- Combinations are selections where the order does not matter.
Combination
- Combination is the selection of items from a larger set where the order does not matter.
- The formula for combinations is nCr = n! / (r!(n - r)!).
- nCr represents the number of combinations.
- N is the number of total objects in the set.
- R is the number of choosing items in the set.
Probability
- Probability is how likely something is to happen.
- Probability (P(A)) = Number of favorable outcomes / Total number of possible outcomes.
- An experiment is an activity with observable results.
- Outcomes are the result of an experiment.
- Sample Space is the set of all possible different outcomes of an experiment.
- An event is the subset of all possible outcomes in probability.
- A compound event happens when an event consists of two or more outcomes.
- The probability of zero is the event is impossible.
- The probability of 1 is the event is certain to happen.
Compound Probability
- The probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
Mutually Exclusive Events
- Two events that cannot occur together and are dependent.
Independent Events
- Events that can occur together.
Distance Formula
- The distance formula is d = √((x2 - x1)² + (y2 - y1)²).
- d represents distance.
- (x1, y1) represents the coordinates of the first point.
- (x2, y2) represents the coordinates of the second point.
Midpoint Formula
- The midpoint formula is (xm, ym) = ((x1 + x2) / 2, (y1 + y2) / 2).
- (xm, ym) represents the coordinates of the midpoint.
- (x1, y1) represents the coordinates of the first point.
- (x2, y2) represents the coordinates of the second point.
Equation of a Circle
- The standard form of the equation of a circle is (x - h)² + (y - k)² = r².
- (h, k) represents the center of the circle.
- R represents the radius.
- The general form of the equation is x² + y² + ax + by + c = 0.
- To get the general form, one must start with the standard form.
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