Three flags, each of different colour, are available for a military exercise. Using these flags, different codes can be generated by waving i) 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 colour The maximum number of codes that can be generated is
- A6
- B9
- C15Correct
- D18
Explanation
The total number of codes is the sum of all possible combinations for each of the three scenarios provided.
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Using a single flag: Since there are 3 different colors available, you can generate 3 unique codes.
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Using two flags in sequence: For the first position, you have 3 color choices. For the second position, you have 2 remaining color choices. Multiplying these gives 3 times 2, which equals 6 codes.
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Using three flags in sequence: For the first position, you have 3 choices; for the second, 2 choices; and for the third, 1 choice remaining. Multiplying these gives 3 times 2 times 1, which equals 6 codes.
To find the maximum number of codes, add the results together: 3 plus 6 plus 6 equals 15.
Therefore, the correct option is C.
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