XAT 2017 — QA & DI Question 14
An institute has 5 departments and each department has 50 students. If students are picked up randomly from all 5 departments to form a committee, what should be the minimum number of students in the committee so that at least one department should have representation of minimum 5 students?
Answer & solution
- A
11
- B
15
21
- D
41
- E
None of the above
The five departments of each department has 50 students.
We have to minimise the number of students in the committee so that at least one department should have representation of minimum 5 students
Let us maximise the number of students in the committee so that no department has representation of 5 students. i.e., any department can have maximum 4 students.
∴ If we select 4 students from each department i.e. a total of 20 students, still no department will have representation of 5 students.
Now if we select one more student, we will have representation of 5 students from at least 1 department.
∴ Minimum number of students in the committee so that at least one department should have representation of minimum 5 students is 21.
Hence, option (c).