UPSC Prelims 2007 · General Studies

Question 140: Basic Numeracy

Groups, each containing 3 boys, are to be formed out of 5 boys – A, B, C, D and E – such that no one group contains both C and D together. What is the maximum number of different groups?

AnswerThe answer is (c).

Choose 3 boys out of 5: C(5,3) = 10 groups. Groups containing both C and D are not allowed. Such a group has C, D and one more boy from A, B or E: 3 groups. So the allowed groups are 10 - 3 = 7. Listing them gives the same: ABC, ABD, ABE, ACE, ADE, BCE, BDE.

Why each option is right or wrong

(a) 5 is too few; the count is 7.
(b) 6 is too few; the count is 7.
(c) Correct: 10 - 3 = 7.
(d) 8 is too many; the count is 7.

Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2007, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.