LFM Stats And Pure

csat-suneung 2007 Q26 (Discrete Mathematics) 3 marks Distribution of Objects into Bins/Groups View

In how many ways can 9 identical candies be distributed into 5 identical bags such that no bag is empty? [3 points]
(1) 8
(2) 7
(3) 6
(4) 5
(5) 4

csat-suneung 2008 Q9 3 marks Selection and Task Assignment View

A music concert is divided into Part 1 and Part 2, with 2 solo teams, 2 ensemble teams, and 3 choir teams performing in total. The performance order of the 7 teams is to be determined according to the following two conditions.
(A) In Part 1, 3 teams perform in the order: solo, ensemble, choir.
(B) In Part 2, 4 teams perform in the order: solo, ensemble, choir, choir. What is the number of ways to determine the performance order for this music concert? [3 points]
(1) 18
(2) 20
(3) 22
(4) 24
(5) 26

csat-suneung 2008 Q25 4 marks Selection with Group/Category Constraints View

A training center operates 5 different types of experience programs. Two participants A and B, who participated in the programs at this training center, each want to select 2 types from the 5 types of experience programs. Find the number of cases where A and B select exactly one type of experience program in common. [4 points]

csat-suneung 2008 Q25 4 marks Selection with Group/Category Constraints View

A training center operates five different types of experience programs. Participants A and B each want to select 2 types from the 5 types of experience programs. Find the number of cases where A and B select exactly one type in common. [4 points]

csat-suneung 2009 Q15 4 marks Distribution of Objects into Bins/Groups View

A certain volunteer service center operates the following 4 volunteer activity programs every day.

Program	A	B	C	D
Volunteer Activity Hours	1 hour	2 hours	3 hours	4 hours

Chulsu wants to participate in one program each day for 5 days at this volunteer service center and create a volunteer activity plan so that the total volunteer activity hours is 8 hours. How many different volunteer activity plans can be created? [4 points]
(1) 47
(2) 44
(3) 41
(4) 38
(5) 35

csat-suneung 2009 Q15 4 marks Counting Integer Solutions to Equations View

A certain volunteer service center operates the following four volunteer activity programs every day.

Program	A	B	C	D
Volunteer Activity Hours	1 hour	2 hours	3 hours	4 hours

Chulsu wants to participate in one program each day for 5 days at this volunteer service center and create a volunteer activity plan so that the total volunteer activity hours is 8 hours. How many different volunteer activity plans can be created? [4 points]
(1) 47
(2) 44
(3) 41
(4) 38
(5) 35

csat-suneung 2009 Q28b 3 marks Combinatorial Probability View

(Probability and Statistics) There are 9 balls in a bag, each labeled with a natural number from 1 to 9. When 4 balls are randomly drawn simultaneously from the bag, what is the probability that the sum of the largest and smallest numbers on the drawn balls is at least 7 and at most 9? [3 points]
(1) $\frac{5}{9}$
(2) $\frac{1}{2}$
(3) $\frac{4}{9}$
(4) $\frac{7}{18}$
(5) $\frac{1}{3}$

csat-suneung 2011 Q6 3 marks Distribution of Objects to Positions or Containers View

At a certain event venue, there are 5 locations where one banner can be installed at each location. There are three types of banners: A, B, and C, with 1 banner of type A, 4 banners of type B, and 2 banners of type C. When selecting and installing 5 banners at the 5 locations to satisfy the following conditions, how many possible cases are there? (Note: Banners of the same type are not distinguished from each other.) [3 points] (가) Banner A must be installed. (나) Banner B must be installed in at least 2 locations.
(1) 55
(2) 65
(3) 75
(4) 85
(5) 95

csat-suneung 2011 Q17 4 marks Combinatorial Probability View

There are 2 students each from Korea, China, and Japan. When these 6 students each randomly select and sit in one of 6 seats with assigned seat numbers as shown in the figure, what is the probability that the two students from the same country sit such that the difference in their seat numbers is 1 or 10? [4 points]

11

12

13

21

22

23

(1) $\frac { 1 } { 20 }$
(2) $\frac { 1 } { 10 }$
(3) $\frac { 3 } { 20 }$
(4) $\frac { 1 } { 5 }$
(5) $\frac { 1 } { 4 }$

csat-suneung 2011 Q20 3 marks Partitioning into Teams or Groups View

When 6 different balls are placed 3 each in two baskets A and B, how many possible outcomes are there? [3 points]

csat-suneung 2011 Q27 (Probability and Statistics) 3 marks Combinatorial Probability View

In a table tennis competition with 4 male table tennis players and 4 female table tennis players, when 2 people are randomly selected to form 4 teams, what is the probability that exactly 2 teams consist of 1 male and 1 female? [3 points]
(1) $\frac { 3 } { 7 }$
(2) $\frac { 18 } { 35 }$
(3) $\frac { 3 } { 5 }$
(4) $\frac { 24 } { 35 }$
(5) $\frac { 27 } { 35 }$

csat-suneung 2012 Q5 3 marks Counting Arrangements with Run or Pattern Constraints View

When arranging 5 white flags and 5 blue flags in a line, how many ways are there to place white flags at both ends? (Note: flags of the same color are indistinguishable from each other.) [3 points]
(1) 56
(2) 63
(3) 70
(4) 77
(5) 84

csat-suneung 2012 Q22 3 marks Basic Combination Computation View

For a natural number $r$, when ${}_{3}\mathrm{H}_{r} = {}_{7}\mathrm{C}_{2}$, find the value of ${}_{5}\mathrm{H}_{r}$. [3 points]

csat-suneung 2013 Q12 3 marks Distribution of Objects to Positions or Containers View

In how many ways can 4 bottles of the same type of juice, 2 bottles of the same type of water, and 1 bottle of milk be distributed to 3 people without remainder? (Note: Some people may not receive any bottles.) [3 points]
(1) 330
(2) 315
(3) 300
(4) 285
(5) 270

csat-suneung 2013 Q29 4 marks Combinatorial Probability View

In the following seating chart, 4 female students and 4 male students are randomly assigned to 8 seats excluding the seat at row 2, column 2, with one person per seat. Find the value of $70p$, where $p$ is the probability that at least 2 male students are seated adjacent to each other. (Two people are considered adjacent if they are next to each other in the same row or directly in front or behind each other in the same column.) [4 points]

csat-suneung 2014 Q9 3 marks Counting Integer Solutions to Equations View

When selecting 5 numbers from the digits $1,2,3,4$ with repetition allowed, how many cases are there where the digit 4 appears at most once? [3 points]
(1) 45
(2) 42
(3) 39
(4) 36
(5) 33

csat-suneung 2014 Q18 4 marks Counting Integer Solutions to Equations View

There are 8 white ping-pong balls and 7 orange ping-pong balls to be distributed entirely among 3 students. In how many ways can the balls be distributed so that each student receives at least one white ball and at least one orange ball? [4 points]
(1) 295
(2) 300
(3) 305
(4) 310
(5) 315

csat-suneung 2015 Q18 4 marks Counting Integer Solutions to Equations View

How many ordered pairs $( x , y , z , w )$ of non-negative integers satisfy the system of equations $$\left\{ \begin{array} { l } x + y + z + 3 w = 14 \\ x + y + z + w = 10 \end{array} \right.$$ ? [4 points]
(1) 40
(2) 45
(3) 50
(4) 55
(5) 60

csat-suneung 2015 Q25 4 marks Counting Integer Solutions to Equations View

Find the number of all ordered pairs $( a , b , c )$ of natural numbers satisfying the following conditions. [4 points] (가) $a \times b \times c$ is odd. (나) $a \leq b \leq c \leq 20$

csat-suneung 2016 Q14 4 marks Selection with Arithmetic or Divisibility Conditions View

For three integers $a , b , c$ satisfying $$1 \leq | a | \leq | b | \leq | c | \leq 5$$ what is the number of all ordered pairs $( a , b , c )$? [4 points]
(1) 360
(2) 320
(3) 280
(4) 240
(5) 200

csat-suneung 2016 Q17 4 marks Counting Integer Solutions to Equations View

How many ordered pairs $( a , b , c , d , e )$ of non-negative integers satisfy the following conditions? [4 points] (가) Among $a , b , c , d , e$, the number of 0's is 2. (나) $a + b + c + d + e = 10$
(1) 240
(2) 280
(3) 320
(4) 360
(5) 400

csat-suneung 2017 Q22 3 marks Basic Combination Computation View

Find the value of ${}_{4}\mathrm{H}_{2}$. [3 points]

csat-suneung 2017 Q27 4 marks Counting Integer Solutions to Equations View

Find the number of all ordered pairs $( a , b , c )$ of non-negative integers satisfying the following conditions. [4 points] (가) $a + b + c = 7$ (나) $2 ^ { a } \times 4 ^ { b }$ is a multiple of 8.

csat-suneung 2018 Q22 3 marks Basic Combination Computation View

Find the value of ${}_{5}\mathrm{C}_{3}$. [3 points]

csat-suneung 2018 Q22 3 marks Basic Combination Computation View

Find the value of ${ } _ { 5 } \mathrm { C } _ { 3 }$. [3 points]

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LFM Stats And Pure

Completing the square and sketching 80

Inequalities 215

Discriminant and conditions for roots 106

Solving quadratics and applications 106

Curve Sketching 295

Factor & Remainder Theorem 90

Polynomial Division & Manipulation 44

Binomial Theorem (positive integer n) 244

Function Transformations 65

Composite & Inverse Functions 249

Partial Fractions 22

Generalised Binomial Theorem 16

Generalised Binomial Theorem and Partial Fractions 3

Complex Numbers Arithmetic 283

Complex Numbers Argand & Loci 135

Permutations & Arrangements 276

Combinations & Selection 268

Measures of Location and Spread 233

Probability Definitions 413

Tree Diagrams 5

Principle of Inclusion/Exclusion 23

Independent Events 51

Conditional Probability 127

Discrete Probability Distributions 210

Binomial Distribution 107

Geometric Distribution 11

Hypergeometric Distribution 10

Negative Binomial Distribution 2

Modelling and Hypothesis Testing 38

Hypothesis test of binomial distributions 12

Data representation 29

Continuous Probability Distributions and Random Variables 30

Continuous Uniform Random Variables 15

Geometric Probability 28

Normal Distribution 96

Approximating Binomial to Normal Distribution 7

Sign Change & Interval Methods 74

Fixed Point Iteration 12