A table consisting of two rows and 7 cells is given in the figure.
Patterns are created by painting 4 cells of this table black.
How many different patterns are there such that each row has at least one painted cell?
A) 26
B) 28
C) 30
D) 32
E) 34

Let A be a subset of the set $\{ 1,2,3,4,5,6,7 \}$. $$A \cap \{ 5,6,7 \}$$ The elements of the set are odd numbers.\ Accordingly, how many three-element sets A satisfy this condition?\ A) 12\ B) 14\ C) 16\ D) 18\ E) 20

If the arrangement of letters in a word from left to right is the same as from right to left, this word is called a palindrome word.
For example; NEDEN is a palindrome word.
Engin will create a 5-letter palindrome word using each of 3 distinct vowels and 4 distinct consonants as many times as he wants. In this word, two vowels should not be adjacent and two consonants should not be adjacent either.
Accordingly, how many different palindrome words can Engin create that satisfy these conditions?
A) 72 B) 84 C) 96 D) 108 E) 120

Let A and B be non-empty sets consisting of digits. If
$$A \cap B = A \cap \{ 0,2,4,6,8 \}$$
equality is satisfied, then A is called the common-intersection set of B. Given that set A is the common-intersection set of
$$B = \{ 0,1,2,3,4 \}$$
how many different sets A are there?
A) 3
B) 7
C) 15
D) 31
E) 63

An exam consisting of a total of 8 questions, with 4 questions each in the verbal and quantitative sections, has the following statement in its booklet: ``To pass the exam, you must answer at least 5 questions correctly in total, with at least 2 questions from each of the verbal and quantitative sections.'' Sevcan, who read this statement incompletely, randomly selected 5 out of 8 questions on the exam and answered each question she selected correctly.
Accordingly, what is the probability that Sevcan passes the exam?
A) $\frac{3}{4}$
B) $\frac{4}{5}$
C) $\frac{5}{6}$
D) $\frac{6}{7}$
E) $\frac{7}{8}$

Kerem randomly selects 3 numbers using the buttons shown in the figure to create the password for his locker, such that each is in a different row and different column.
Accordingly, what is the probability that all of the numbers Kerem selected are odd?
A) $\frac{1}{2}$
B) $\frac{1}{3}$
C) (from figure)
D) $\frac{5}{9}$
E) $\frac{4}{27}$

Let $a$ and $b$ be digits. Given the sets
$$\begin{aligned} & A = \{ 5,6,7,8,9 \} \\ & B = \{ 1,4,5,7 \} \\ & C = \{ a , b \} \end{aligned}$$
If the number of elements in the Cartesian product $(A \cup C) \times (B \cup C)$ is 28, what is the sum $a + b$?
A) 5
B) 6
C) 8
D) 9
E) 11

A project team of 100 people has a certain number of projects, and everyone in the team will be assigned to some of these projects. It is desired that everyone in the team works on an equal number of projects, but no two people work on exactly the same projects. This condition cannot be satisfied if everyone works on 3 projects, but it can be satisfied if everyone works on 4 projects.
Accordingly, how many projects does the team have?
A) 6
B) 7
C) 8
D) 9
E) 10

In a mathematics class, the teacher asks Veli to calculate in how many different ways 3 students can be selected, Yasin to calculate in how many different ways 5 students can be selected, and Zeynep to calculate in how many different ways 11 students can be selected from the students in the class. All three students calculated the requested numbers correctly.
Given that the numbers found by Yasin and Zeynep are the same positive integer, what is the number found by Veli?
A) 364 B) 560 C) 688 D) 816 E) 960

In a course, the weekly lesson durations of 7 lessons, each with different lesson times, are given in the table below.

Lesson	Duration (hours)
Lesson 1	5
Lesson 2	4
Lesson 3	4
Lesson 4	5
Lesson 5	3
Lesson 6	5
Lesson 7	5

Aslı, who enrolled in this course, wants to take four different lessons such that the total weekly lesson duration is 17 hours.
Accordingly, in how many different ways can Aslı select the lessons she will take?
A) 8 B) 10 C) 12 D) 16 E) 18

Melisa will stack 10 circular cardboards with radii $1\text{ cm}, 2\text{ cm}, 3\text{ cm}, \cdots, 10\text{ cm}$ on a table with their centers coinciding, where each has a different natural number radius.
In how many different ways can Melisa arrange them so that when viewed from above, exactly one of the circles is completely hidden?
A) 36 B) 40 C) 45 D) 48 E) 54

Duru observed that she was present in 45 of all three-person groups that could be formed from the students in her class.
Accordingly, in how many of all three-person groups that could be formed from the students in Duru's class is Duru not present?
A) 20
B) 35
C) 90
D) 105
E) 120