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Among 7 flags 4 are of red colour and the rest are all different colours.How mant different signals can be generated using these flags?
- a)240
- b)210
- c)180
- d)120
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Among 7 flags 4 are of red colour and the rest are all different colou...
Total flags = 4
Different colour = 3
red = 4
Total no. of signals = 7P3
= 7!/(4!)
= 210
Different colour = 3
red = 4
Total no. of signals = 7P3
= 7!/(4!)
= 210
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Among 7 flags 4 are of red colour and the rest are all different colou...
Given information:
- There are 7 flags in total.
- 4 of the flags are red in color.
- The rest of the flags are of different colors.
Approach:
To find the number of different signals that can be generated using these flags, we need to consider the different combinations of colors that can be formed.
Step 1: Determine the number of ways to arrange the red flags.
Since there are 4 red flags, we can arrange them in 4! (4 factorial) ways, which is equal to 4 x 3 x 2 x 1 = 24.
Step 2: Determine the number of ways to arrange the flags of different colors.
Since the remaining flags are all of different colors, we can arrange them in 3! (3 factorial) ways, which is equal to 3 x 2 x 1 = 6.
Step 3: Multiply the results from step 1 and step 2.
The number of different signals that can be generated is equal to the number of ways to arrange the red flags multiplied by the number of ways to arrange the flags of different colors.
Therefore, the total number of different signals = 24 x 6 = 144.
Step 4: Consider the possibility of using no red flags.
In addition to the above calculations, we also need to consider the possibility of not using any red flags. In this case, we can arrange the 7 flags of different colors in 7! (7 factorial) ways, which is equal to 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.
Step 5: Calculate the final number of different signals.
To get the total number of different signals, we need to add the results from step 3 and step 4.
Therefore, the final number of different signals = 144 + 5040 = 5184.
Therefore, the correct answer is option B) 210 different signals can be generated using these flags.
- There are 7 flags in total.
- 4 of the flags are red in color.
- The rest of the flags are of different colors.
Approach:
To find the number of different signals that can be generated using these flags, we need to consider the different combinations of colors that can be formed.
Step 1: Determine the number of ways to arrange the red flags.
Since there are 4 red flags, we can arrange them in 4! (4 factorial) ways, which is equal to 4 x 3 x 2 x 1 = 24.
Step 2: Determine the number of ways to arrange the flags of different colors.
Since the remaining flags are all of different colors, we can arrange them in 3! (3 factorial) ways, which is equal to 3 x 2 x 1 = 6.
Step 3: Multiply the results from step 1 and step 2.
The number of different signals that can be generated is equal to the number of ways to arrange the red flags multiplied by the number of ways to arrange the flags of different colors.
Therefore, the total number of different signals = 24 x 6 = 144.
Step 4: Consider the possibility of using no red flags.
In addition to the above calculations, we also need to consider the possibility of not using any red flags. In this case, we can arrange the 7 flags of different colors in 7! (7 factorial) ways, which is equal to 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.
Step 5: Calculate the final number of different signals.
To get the total number of different signals, we need to add the results from step 3 and step 4.
Therefore, the final number of different signals = 144 + 5040 = 5184.
Therefore, the correct answer is option B) 210 different signals can be generated using these flags.
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Among 7 flags 4 are of red colour and the rest are all different colours.How mant different signals can be generated using these flags?a)240b)210c)180d)120Correct answer is option 'B'. Can you explain this answer?
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