Pigeonhole Principle in Committee Selection
XAT 2017 · Quantitative Ability & Data Interpretation · Easy · Permutations and Combinations
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.
C
Explanation
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 = . Adding 1 more student guarantees at least one department has 5 students. Minimum number required = .
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