Question

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?

A.
11
B.
15
C.
21
D.
41
E.
None of the above.

Accepted Answer

C. By the Pigeonhole Principle, to avoid any department having 5 or more students, maximum number of students picked per department is 4. For 5 departments, maximum students selected without any department reaching 5 = $5 	imes 4 = 20$. Adding 1 more student guarantees at least one department has 5 students. Minimum number required = $20 + 1 = 21$.

Pigeonhole Principle in Committee Selection

Explanation

Practise this under exam conditions