Basic Combination Computation

The question asks to directly compute a single combination C(n,r) or permutation P(n,r) value, with no additional constraints or conditions beyond choosing r items from n.

turkey-yks 2021 Q29 View
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
turkey-yks 2024 Q29 View
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