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Four female friends & four male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with men & women alternating. How many possible arrangements may she chose?
- a)40320
- b)1680
- c)1152
- d)576
- e)70
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Four female friends & four male friends will be pictured in a adve...
Now any of the alternate 4 places can be filled by 4 male or female in 4!
Similarily,
other 4 alternate places can be filled in 4!
Hence required probability= 2*4!*4!=1152
Similarily,
other 4 alternate places can be filled in 4!
Hence required probability= 2*4!*4!=1152
Most Upvoted Answer
Four female friends & four male friends will be pictured in a adve...
Arranging Male and Female Friends in a Row
To line up the four female friends and four male friends in a row with men and women alternating, we can think of them as blocks of males and females that need to be arranged in a specific order.
Arranging Blocks of Male and Female Friends
- Since we have four female friends and four male friends, there are 4! ways to arrange the females and 4! ways to arrange the males.
- However, these blocks can be arranged in different ways. We can start with either a male or a female, so there are 2 ways to arrange the blocks.
Total Number of Arrangements
- To find the total number of arrangements, we multiply the number of ways to arrange the females, males, and blocks together: 4! * 4! * 2 = 1152
Therefore, the photographer has 1152 possible arrangements to choose from to line up the four female friends and four male friends in a row with men and women alternating. So, the correct answer is option 'C' - 1152.
To line up the four female friends and four male friends in a row with men and women alternating, we can think of them as blocks of males and females that need to be arranged in a specific order.
Arranging Blocks of Male and Female Friends
- Since we have four female friends and four male friends, there are 4! ways to arrange the females and 4! ways to arrange the males.
- However, these blocks can be arranged in different ways. We can start with either a male or a female, so there are 2 ways to arrange the blocks.
Total Number of Arrangements
- To find the total number of arrangements, we multiply the number of ways to arrange the females, males, and blocks together: 4! * 4! * 2 = 1152
Therefore, the photographer has 1152 possible arrangements to choose from to line up the four female friends and four male friends in a row with men and women alternating. So, the correct answer is option 'C' - 1152.
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