Question Detail
Question
What is the number of signals that can be sent by 6 flags of different colours taking one or more at a time?
Correct Answer
Option D is the correct answer.
Detailed Explanation
Since the flags are of different colours and form signals, the order in which they are displayed matters. This is a permutation problem.The number of signals that can be sent by taking:1 flag at a time: 6P1 = 62 flags at a time: 6P2 = 6 × 5 = 303 flags at a time: 6P3 = 6 × 5 × 4 = 1204 flags at a time: 6P4 = 6 × 5 × 4 × 3 = 3605 flags at a time: 6P5 = 6 × 5 × 4 × 3 × 2 = 7206 flags at a time: 6P6 = 6 × 5 × 4 × 3 × 2 × 1 = 720Total number of signals = 6 + 30 + 120 + 360 + 720 + 720 = 1956.
Hint
When the order of selection matters (as in forming signals with different flags), use permutations. Sum the permutations for selecting 1 flag, 2 flags, and so on, up to all flags.