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Question
Given four flags of different colours, how many different signals can be generated if each signal requires the use of three flags, one below the other?
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Solution
| First flag |
| Second flag |
| Third flag |
Number of flags = 4
Number of flags required for a signal = 3
The total number of signals is equal to the number of ways of filling 3 places in succession by 4 flags of different colours.
Number of ways of filling the top place using 4 different colour flags is 4 ways.
Number of ways of filling the middle place using the remaining 3 different colour flags is 3 ways.
Number of ways of filling the bottom place using the remaining 2 different colour flags is 2 ways.
Therefore, by fundamental principle of multiplication,
The total number of signals = 4 × 3 × 2 = 24 ways
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