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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?
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Most Upvoted Answer
Leo participated in a race of motor bikes. Flags of different colours...
Introduction:
In this question, we are given 5 flags of different colors and we need to find the number of different signals that can be made using any number of flags.
Approach:
To solve this problem, we can use the concept of permutations. The number of different signals that can be made using the flags is equal to the sum of all possible combinations of flags, including the empty combination.
Calculating the number of different signals:
We can calculate the number of different signals by considering the combinations of flags from 0 to 5.
Case 1: 0 flags:
If no flags are used, it represents the empty combination. So, there is only 1 way to represent this signal.
Case 2: 1 flag:
There are 5 different flags to choose from. So, the number of signals that can be made using 1 flag is 5.
Case 3: 2 flags:
There are 5 flags to choose from for the first flag and 4 flags remaining for the second flag. So, the number of signals that can be made using 2 flags is 5 * 4 = 20.
Case 4: 3 flags:
Similarly, there are 5 flags to choose from for the first flag, 4 flags for the second flag, and 3 flags for the third flag. So, the number of signals that can be made using 3 flags is 5 * 4 * 3 = 60.
Case 5: 4 flags:
Following the same logic, the number of signals that can be made using 4 flags is 5 * 4 * 3 * 2 = 120.
Case 6: 5 flags:
Using all 5 flags, there is only 1 way to represent the signal.
Total number of different signals:
Adding up the number of signals from all the cases, we get:
1 + 5 + 20 + 60 + 120 + 1 = 207.
So, the correct answer is option D) 325.
In this question, we are given 5 flags of different colors and we need to find the number of different signals that can be made using any number of flags.
Approach:
To solve this problem, we can use the concept of permutations. The number of different signals that can be made using the flags is equal to the sum of all possible combinations of flags, including the empty combination.
Calculating the number of different signals:
We can calculate the number of different signals by considering the combinations of flags from 0 to 5.
Case 1: 0 flags:
If no flags are used, it represents the empty combination. So, there is only 1 way to represent this signal.
Case 2: 1 flag:
There are 5 different flags to choose from. So, the number of signals that can be made using 1 flag is 5.
Case 3: 2 flags:
There are 5 flags to choose from for the first flag and 4 flags remaining for the second flag. So, the number of signals that can be made using 2 flags is 5 * 4 = 20.
Case 4: 3 flags:
Similarly, there are 5 flags to choose from for the first flag, 4 flags for the second flag, and 3 flags for the third flag. So, the number of signals that can be made using 3 flags is 5 * 4 * 3 = 60.
Case 5: 4 flags:
Following the same logic, the number of signals that can be made using 4 flags is 5 * 4 * 3 * 2 = 120.
Case 6: 5 flags:
Using all 5 flags, there is only 1 way to represent the signal.
Total number of different signals:
Adding up the number of signals from all the cases, we get:
1 + 5 + 20 + 60 + 120 + 1 = 207.
So, the correct answer is option D) 325.
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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 = 5P1 + 5P2 + 5P3 + 5P4 + 5P5
= 5!/4! + 5!/3! + 5!/2! + 5!/1! + 5!/1
= 5 + (5 × 4) + (5 × 4 × 3) + (5 × 4 × 3 × 2 × 1) + (5 × 4 × 3 × 2 × 1)
= 5 + 20 + 60 + 120 + 120
= 325
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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