UPSC Prelims 2003 Q4: Science & Technology – Quantitative Aptitude
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
- (a) 6
- (b) 9
- (c) 15
- (d) 18
Answer: (c) 15
Explanation
Codes made by waving flags
| Way of waving | Number of codes |
|---|---|
| A single flag | 3 colours, so 3 codes |
| Any two flags in sequence | 3 x 2 = 6 codes |
| Three flags in sequence | 3 x 2 x 1 = 6 codes |
| Total | 3 + 6 + 6 = 15 |
The maximum number of codes is 3 + 6 + 6 = 15, counting the single-flag codes, the ordered two-flag codes and the ordered three-flag codes together.
Answer: (c) 15.
Why each option is right or wrong
- (a) Incorrect. 6 counts only the sequences of three flags.
- (b) Incorrect. 9 counts only the single and two-flag codes.
- (c) CORRECT. 3 + 6 + 6 = 15 codes.
- (d) Incorrect. 18 double counts some sequences.
Key point
Add the arrangements of 1, 2 and 3 flags: 3P1 + 3P2 + 3P3.
Remember
3P1 + 3P2 + 3P3 = 3 + 6 + 6 = 15 codes.
Common mistakes
- Counting only three-flag sequences.
- Using combinations instead of ordered sequences.
- Forgetting the single-flag codes in the total.
Exam tip
Order matters in codes, so use permutations.
Sources
- NCERT Class XI Mathematics — Permutations and Combinations
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Permutations and Combinations)