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 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