O Flashcards by Axzye Lavender

What is referred to as an arrangement of objects in definite order?

Permutation

A permutation considers the order of arrangement.

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Which situation illustrates permutation?

Creating a password in google account

The order of characters in a password matters.

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Which of the following is equivalent to nPr?

n!/(n-r)!

This formula calculates the number of permutations of n items taken r at a time.

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Which of the following illustrates 5P2?

5! / (5-2)!

This expression represents the number of ways to arrange 2 items from a set of 5.

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What expression gives the number of ways in arranging 6 different books on a shelf?

The factorial notation accounts for all possible arrangements.

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Which concept is involved when the word ‘CARE’ taken 4 at a time equals 24?

Permutation

The arrangement of letters considers the order.

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What concept is used in the problem: ‘There are 10 finalists for the Math Contest, the medals will be given to the top three’?

Permutation

The order of medal winners matters.

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In how many ways can prizes be won if there are 7 contestants?

7 x 6 x 5

This represents the number of ways to award prizes to the top three contestants.

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How many ways can Juan choose the order of his activities in Filipino, English, Math, and Science?

This is calculated by 4!, the factorial of the number of activities.

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How many distinct permutations are there in the word ‘DAD’?

The calculation accounts for repeated letters.

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In how many ways can 6 children stand in a circle to play a game?

120

Circular arrangements reduce the total arrangements by a factor equal to the number of children.

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Which among the following is equal to 5P3?

This represents the number of ways to arrange 3 items from a set of 5.

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If P(n,4) = 5040, then n = _______.

This is derived from the permutation formula.

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What is defined as the number of possible arrangements in a group of items where order is NOT important?

Combination

Combinations disregard order in selections.

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Which of the following is the formula for nCr?

n! / (n-r)! r!

This formula calculates combinations.

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Which of the following illustrates a combination?

Selecting five students to attend in Math Club

The selection does not consider the order of students.

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Which of the following is NOT a combination?

Number of even 4 digits without repetition

This involves the arrangement of numbers, which is a permutation.

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What best describes the statement, ‘Picking a team of four people out of a group of 16’?

Combination

The order of selection does not matter.

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How many straight lines can be drawn using the five points (M, N, O, P, and Q) where no three points are collinear?

This is calculated using the combination formula.

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Evaluate 12C3.

220

This uses the combination formula to find the number of ways to choose 3 from 12.

Juan has 6 close friends. He has only 3 tickets for the SB 19 concert. In how many ways can he choose 3 tickets for his friends?

This is a combination problem.

How many ways can 5 yellow beads, 3 red beads, and 2 green beads be arranged on a bracelet without lock if the only difference in beads is color?

126

This involves permutations of multiset.

In how many ways can 6 balls be chosen from a box containing 5 red, 7 green, and 6 yellow balls if there should be 2 balls of each color?

3150

This is calculated based on combinations of colored balls.

Find the number of different ways of placing 9 marbles in a row given that 3 are red, 4 are green, and 2 yellow.

1260

This uses the formula for permutations of a multiset.

What is defined as the set of all possible outcomes of an experiment or activity?

Sample Space ## Footnote The sample space encompasses all potential results.

If two coins were tossed, what is the sample space (S)?

{HH, HT, TH, TT} ## Footnote This includes all combinations of heads and tails.

Let A be prime numbers and B be even numbers from a bag containing balls numbered 1 to 10. What is A ∩ B?

{2} ## Footnote The intersection includes numbers that are both prime and even.

If a survey shows that A is male students and B are visual learners, what is A ∩ B?

12 ## Footnote This is determined based on survey data.

How many possible outcomes are there if Santi randomly picks one shirt from 25 shirts?

25 ## Footnote Each shirt represents a unique outcome.

What is the probability that Santi will randomly pick a red shirt?

4/25 ## Footnote This is calculated based on the ratio of red shirts to total shirts.

What is the probability that Santi will pick a blue shirt or a red shirt?

12/25 ## Footnote This combines the probabilities of blue and red shirts.

Two events are ___________________ if both events cannot occur at the same time.

Mutually Exclusive ## Footnote Mutually exclusive events cannot happen simultaneously.

Which illustrates mutually exclusive events?

I and II ## Footnote Getting heads and tails on a coin toss and rolling different numbers on a die are mutually exclusive.

Which illustrates non-mutually exclusive events?

III only ## Footnote Drawing a king and a diamond can occur at the same time.

If a student is chosen at random, what is the probability that the student prefers both Mathematics and Science?

1/4 ## Footnote This is calculated based on survey results.

What is the probability of drawing a heart or a diamond in an ordinary deck of cards?

1/2 ## Footnote There are 26 cards that are either hearts or diamonds.

What is the probability that a number selected from the first 15 positive integers is exactly divisible by 3 or 5?

7/15 ## Footnote This is calculated based on the count of numbers divisible by 3 or 5.

What is the probability that a number selected from the first 15 positive integers is exactly divisible by 3 and 5?

1/15 ## Footnote This is determined by the least common multiple.

What type of event does the activity 'A marble was drawn in a bag, replaced and another was drawn' illustrate?

Independent Events ## Footnote The outcome of the first draw does not affect the second.

What is the probability that two randomly pulled socks from a drawer of colored socks will be black?

9/38 ## Footnote This calculation is based on combinations of drawing two black socks.

What is the probability that the socks chosen are both black or both blue?

6/19 ## Footnote This combines the probabilities of both color choices.

What is the probability that a 2 will show on the first die and a 3 will show on the second die when two dice are rolled?

1/36 ## Footnote This is the probability of independent events occurring.

What is the probability of getting a number 7 when a die is rolled?

0 ## Footnote A standard die does not have a 7.

What is the probability that the card drawn is black or queen from a standard deck of 52 cards?

7/13 ## Footnote This includes all black cards and the two queens.

What is the probability of getting heads on all four tosses of a coin tossed 4 times?

1/16 ## Footnote This is calculated as (1/2)^4.

What is the probability that a letter picked from the alphabet is either in the word MATH or in the word TEN?

3/13 ## Footnote This considers the unique letters from both words.

What is the probability that the first performer is a boy, the second is a girl, and the third is another boy from a theater club of 10 boys and 8 girls?

20/153 ## Footnote This is calculated based on the total combinations of performers.

What percentage of the respondents uses Facebook or Instagram based on a survey where 50% use Instagram, 60% use Facebook, and 30% use both?

80% ## Footnote This is calculated using the principle of inclusion-exclusion.

What percentage of the customers likes both sinigang and adobo based on a survey where 60% like sinigang or adobo, 30% favor adobo, and 40% love sinigang?

10% ## Footnote This is derived from the inclusion-exclusion principle.