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
OA C
probability help
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there are 8 places.mitaliisrani wrote: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
OA C
Fix alternate 4 places You may want to start from first place by Female or first by male
hence 2 methods,
now you have two alternate sequence with 4 blanks and 4 female or male
hence its 4! *4!
total required probability= 2*4!*4!=1152
hence C
Hope this helps..!!
The easiest way to solve this is by drawing:
Imagine the row starts from left with a male. You will have 4 people to choose from. Next a female. You have 4 people (4 females) to choose from. Next will be a male, 3 options (since you already chose 1). And female with 3 options etc.. So it will look like :
4-4-3-3-2-2-1-1
The number of possible arrangements from above is 4*4*3*3*2*2*1*1 = 576.
Now you are not done yet. What if the row starts with a female? It will be the same logic and outcome. So there are 576 additional possibilities.
The total answer is 576*2 = 1152
Imagine the row starts from left with a male. You will have 4 people to choose from. Next a female. You have 4 people (4 females) to choose from. Next will be a male, 3 options (since you already chose 1). And female with 3 options etc.. So it will look like :
4-4-3-3-2-2-1-1
The number of possible arrangements from above is 4*4*3*3*2*2*1*1 = 576.
Now you are not done yet. What if the row starts with a female? It will be the same logic and outcome. So there are 576 additional possibilities.
The total answer is 576*2 = 1152
You can choose the 1st person in 8 ways, than you have a constraint - you should choose a person of another GMAT - 4 ways.mitaliisrani wrote: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
OA C
Now we have equal quantity of F&M = 3, so each two next people can be chosen in 3 ways. Then in two ways again two times, and finally we have 1 F and 1 M.
So the answer is 8x4x3x3x2x2x1x1=1152 - Choose C )))
Lets say the photographer chooses male to stand first. So the first position can be chosen in 4 ways. Next position is for a female so again it acn be chosen in 4 ways. Next is a male position and can be chosen out of three remaining males so 3 ways for that. Similarly for next female position 3 ways.The remaining 2 position for males can be chosen in 2 ways. And similarly remaining two female positions can be chosen in 2 ways. So the total arrangement can be done in 4*3*2*4*3*2 = 4!*4!.
Now the photographer can alternatively choose female to stand first and following the above scenario arrangement can take place in 4!*4! ways. So total number of ways of arranging are 4!*4! + 4!*4!=2*4!*4!. Simple maths shows the answer is C
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Now the photographer can alternatively choose female to stand first and following the above scenario arrangement can take place in 4!*4! ways. So total number of ways of arranging are 4!*4! + 4!*4!=2*4!*4!. Simple maths shows the answer is C
If you feel this has been helpful to you please take a moment to click on thank.
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Men and women alternating can be done in the following 2 ways:mitaliisrani wrote: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
OA C
(1) M-W-M-W-M-W-M-W
(2) W-M-W-M-W-M-W-M
For each of the above cases, men can be arranged in 4! ways.
Similarly, women can be arranged in 4! ways.
Therefore, total number of arrangements = 2 * 4! * 4! = 2 * 4 * 3 * 2 * 4 * 3 * 2 = 1,152
The correct answer is C.
Anurag Mairal, Ph.D., MBA
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