Combinatorial Counting (Non-Probability)

The question asks to count the number of paths, arrangements, subsets, or configurations satisfying given constraints without framing the answer as a probability.

turkey-yks 2023 Q15 View
Let $A, B$ and $C$ be digits different from zero and from each other; the sum of the two-digit natural number AB and the two-digit natural number BC equals one less than the two-digit natural number CA.
Accordingly, how many different three-digit natural numbers ABC can be written using the digits A, B, and C that satisfy this condition?
A) 1 B) 2 C) 3 D) 5 E) 6
turkey-yks 2023 Q18 View
Boat trips are organized for visitors who want to visit a tourist island. The boat departs when there are at least 20 passengers and can carry a maximum of 35 passengers. On a particular day, 3 boat trips were organized and a total of 91 passengers were transported. The ratio of the number of passengers transported in the first trip to the number of passengers transported in the second trip is $\frac{4}{5}$.
Accordingly, how many passengers were transported in the third trip?
A) 21 B) 24 C) 28 D) 32 E) 35
turkey-yks 2023 Q20 View
Yeşim organized a poll on social media with a mosque photo she took in Edirne. After a certain period, the number of votes used for some cities and the ratio of the number of votes used for some cities to the total number of votes as a percentage are given. After this distribution, 5 more votes were cast in total, 4 of which were for Edirne and 1 for Istanbul.
Accordingly, what is the percentage of the number of votes cast for Edirne to the total number of votes in the final situation?
A) 36 B) 38 C) 40 D) 42 E) 44
turkey-yks 2023 Q21 View
The campaigns at stationery stores $A$ and $B$, which have the same prices for the same type of products, are as follows.
  • At stationery store A, when a backpack is purchased, a pen case is sold at half price.
  • At stationery store B, when 2 of the same type of product are purchased, a 40\% discount is applied to the 2nd product.

Ege and Deniz took advantage of stationery store A's campaign and each bought one backpack priced at 300 TL and one pen case priced at 120 TL.
If Ege and Deniz had each bought one backpack and one pen case of the same type from stationery store B, how much less would the total amount they paid be compared to what they paid to stationery store A?
A) 30 B) 36 C) 42 D) 48 E) 54
turkey-yks 2023 Q23 View
A painter displayed all of his paintings at his first exhibition and sold some of them. In all subsequent exhibitions, this painter displayed the paintings that were not sold at the previous exhibition together with new paintings he created.
The painter sold $\frac{3}{5}$ of the paintings he displayed at each exhibition. Also, for each exhibition after the first, he created as many new paintings as the number of paintings remaining from the previous exhibition.
Given that the painter sold 96 paintings at his 3rd exhibition, how many paintings did he display at his first exhibition?
A) 100 B) 150 C) 200 D) 250 E) 300
turkey-yks 2023 Q24 View
Aras divides all of his marbles into groups of 3 and obtains a two-digit natural number AB, and divides them into groups of 8 and obtains a two-digit natural number BA.
According to this, if Aras divides all the marbles he has into groups such that each group has an equal number of marbles, which of the following could be the number of groups he obtains?
A) 40 B) 48 C) 54 D) 56 E) 60
turkey-yks 2023 Q25 View
Serkan's wardrobe contains three types of clothing: shirt ($G$), pants ($P$), and jacket (C). The numerical distribution of these clothes initially in the wardrobe is shown in the pie chart below.
Serkan takes a certain number of clothes from his wardrobe to dry cleaning. In the final situation, the numerical distribution of the clothes remaining in Serkan's wardrobe shown in the pie chart is the same as the initial one.
Given that Serkan initially had 5 jackets in his wardrobe and he took 1 of these jackets to dry cleaning, how many shirts are left in Serkan's wardrobe?
A) 8 B) 10 C) 15 D) 18 E) 20
turkey-yks 2023 Q26 View
When Ali dede, whose grandfather's restaurant was founded in 1949, came to the restaurant, he said the following sentence to his grandson.
``In the year this restaurant was founded, I was 11 years old, and in the year you were born, this place had been in service for 40 years.''
Accordingly, what is the sum of the ages of Ali dede and his grandson in 2022?
A) 101 B) 105 C) 109 D) 113 E) 117
turkey-yks 2023 Q28 View
A tour company has offered three different transportation options: train, bus, and airplane for a tour it will organize to Adana. The company's per-person fare information for this tour according to transportation vehicles and some information about the number of people who chose these transportation vehicles are given in the table below.
\cline{2-4} \multicolumn{1}{c|}{}TrainBusAirplane
Fare (TL)300750
Number of People108

Among the people who participated in this tour; the number of those who chose the bus for transportation is equal to 6 times the number of those who chose the airplane. Also, in this tour, the total fare paid by those who chose the train for transportation is equal to the total fare paid by those who chose the airplane.
Accordingly, what is the total number of people going to Adana with this tour?
A) 165 B) 171 C) 177 D) 183 E) 189
turkey-yks 2025 Q29 View
Aras will complete all of the following activities on a Sunday: exercising, watching a movie, doing homework, doing household chores, and taking a bath. Aras does not start one activity before completing another. Aras must take a bath after exercising, and must complete his homework and household chores before watching a movie.
According to this, in how many different ways can Aras arrange these five activities?
A) 10 B) 15 C) 20 D) 25 E) 30