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Three flags each of different colours are available for a military exercise, Using these flags different codes can be generated by waving I. Single flag of different colours II. Any two flags in a different sequence of colours. III. three flags in a different sequence of colours. The maximum number of codes that can be generated is.

Correct answer: C. 15

  • A. 6
  • B. 9
  • C. 15
  • D. 18

Explanation

With three distinct flags, single-flag codes give 3 arrangements, two-flag codes give 3P2 = 3 x 2 = 6 arrangements, and three-flag codes give 3P3 = 3 x 2 x 1 = 6 arrangements. The total is 3 + 6 + 6 = 15 codes. The likely wrong choice is 6, which counts only the arrangements using all three flags and ignores the one- and two-flag codes.

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