UPSC Prelims 2003 · General Studies
Question 4: Basic Numeracy
Three flags, each of different colour, are available for a military exercise. Using these flags, different codes can be generated by waving i) a single flag of different colours, or ii) any two flags in a different sequence of colours, or iii) three flags in a different sequence of colours. The maximum number of codes that can be generated is
AnswerThe answer is (c).
Count the codes case by case. One flag: 3 choices. Two flags in a sequence: 3 x 2 = 6 ordered pairs. Three flags in a sequence: 3 x 2 x 1 = 6 orders. Total = 3 + 6 + 6 = 15. Because order matters in the second and third cases, use permutations (3P1 + 3P2 + 3P3), not combinations, which would give only 3 + 3 + 1 = 7.
Why each option is right or wrong
- (a) 6 counts only the three-flag orderings and leaves out single flags and pairs.
- (b) 9 adds singles and pairs (3 + 6) but omits the three-flag sequences.
- (c) Correct: 3 + 6 + 6 = 15.
- (d) 18 overcounts; it does not match the three cases added together.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2003, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.