A group of 4 is to be chosen from 9 students, among whom are Asha and Bela. In how many ways can the group be chosen if Asha must be in the group and Bela must not be in it?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 35
A person who must be in takes one place at once; a person who must be out is simply removed. Only the remaining places are filled from the remaining people.
Asha is in: 3 places are left
Bela is out, and Asha is already placed: \(9-2=7\) students remain
Ways \(\displaystyle =\,^7C_3=\frac{7\times6\times5}{3\times2\times1}=35\)
Why the other options are incorrect
Option (1) 56 — Incorrect. This is \(^8C_3\); it keeps Bela among the students who can be chosen.
Option (3) 126 — Incorrect. This is \(^9C_4\), which ignores both conditions.
Option (4) 21 — Incorrect. This is \(^7C_2\); with Asha in, 3 places are left, not 2.