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Leo participated in a race of motor bikes. Flags of different colours are lowered to give different signals. How many different signals can be made here, using any number of flags from 5 flags of different colours?
  • a)
    5
  • b)
    3125
  • c)
    25
  • d)
    325
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Leo participated in a race of motor bikes. Flags of different colours...
Understanding the Problem
In this scenario, Leo can use 5 flags of different colors to create various signals. Each flag can either be used or not used, leading to different combinations.
Calculating the Total Signals
- Each flag has 2 possibilities: it can either be included in the signal or not.
- With 5 flags, the total combinations would be calculated as follows:
- For Flag 1: 2 options (used or not)
- For Flag 2: 2 options (used or not)
- For Flag 3: 2 options (used or not)
- For Flag 4: 2 options (used or not)
- For Flag 5: 2 options (used or not)
Formula for Combinations
- The total combinations can be expressed as:
- 2^5 = 32 combinations
Excluding the Empty Signal
- However, one of these combinations is the scenario where no flags are used at all, which is not a valid signal.
- Therefore, we need to subtract this one possibility:
Final Calculation
- Total valid signals = 32 - 1 (empty signal) = 31
Understanding the Options
- The answer provided as option 'D' (325) appears to be incorrect based on this reasoning.
- The correct number of valid signals using any number of flags from 5 flags of different colors is 31.
Conclusion
- Leo can create a total of 31 different signals using the 5 flags available, excluding the non-signal of using no flags at all.
Free Test
Community Answer
Leo participated in a race of motor bikes. Flags of different colours...
Signals can be made by using at a time one, two, three, four and five flags.
∴ Total number of signals that can be made
So, 325 signals can be made using five flags.
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Leo participated in a race of motor bikes. Flags of different colours are lowered to give different signals. How many different signals can be made here, using any number of flags from 5 flags of different colours?a)5b)3125c)25d)325Correct answer is option 'D'. Can you explain this answer?
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