Latest Infosys Aptitude Question SOLUTION: In how many ways can 4 boys and 4 girls be arranged in a row such that boys and girls alternate theirpositions (that is, boy girl)?

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In how many ways can 4 boys and 4 girls be arranged in a row such that boys and girls alternate theirpositions (that is, boy girl)?

Asked In Infosys chaitanya (11 years ago)

Unsolved Read Solution (7)

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Read Solution (7) :

priyanka  (11 years ago)

case 1

consider boys are placed in odd positions

b1 g1 b2 g2 b3 g3 b4 g4

the arrangement of girls in 4 even position is 4!
the arrangement of girls in 4 odd position is 4!
therefore possible arrangements are (4!*4!)

case 2


consider girls are placed in odd positions and boys in even position

g1 b1 g2 b2 g3 b3 g4 b4

the arrangement of girls in 4 odd position is 4!
the arrangement of girls in 4 even position is 4!
therefore possible arrangements are (4!*4!)

from case 1 and case 2 , total no of arrangement possible are
(4!*4!)+(4!*4!)
= 576+576
=1152

Is this solution Helpfull? Yes (24) | No (1)  

jomon v j  (11 years ago)

- B1- B2 - B3 - B4-

THE FOUR BOYS CAN BE ARRANGED IN 24 WAYS.NOW THE GIRLS CAN OCCUPY 5 POSITIONS

INDICATED BY THE ´ - ´ THIS CAN BE DONE IN P(5,4) =120 WAYS.

THEREFORE TOTAL NO.OF ARRANGEMENTS =24*120=2880

Is this solution Helpfull? Yes (5) | No (4)  

Yuvaraj  (11 years ago)

96 ways

Let us assume that the arrangement starts with a boy. such as
B1,G1,B2,G2,B3,G3,B4,G4
the boys are at odd places and girls are at even places.
boys in odd places can be arranged in 4P4 ways =>4*3*2*1=24 ways
girls in even places can be arranged in 4P4 ways =>24 ways

Now the girls are at odd places and boys are at even places.
G1,B1,G2,B2,G3,B3,G4,B4
boys at even places can be arranged in 4P4 ways =>24 ways
girls at odd positions can be arranged in 4P4 ways =>24 ways

Totally we can arrange in 24+24+24+24=96ways

Is this solution Helpfull? Yes (3) | No (14)  

Abhradeep Ganguli  (10 years ago)

4 boys can be arranged in 4 fixed place in 4 ways and 4 girls can also be arrangd in 4 ways. so there are 4*4=16 ways. now the arrangement may start with boy or girl so there are 16*2=32 ways

Is this solution Helpfull? Yes (1) | No   

sunil chhuttani  (11 years ago)

ans 676
consider boys are placed in odd positions
b1 g1 b2 g2 b3 g3 b4 g4
4c3*4c3+4c2#4c2+4c1*4c1 = 26
nd for girls is 26
so ans is 676

Is this solution Helpfull? Yes | No (4)  

rahul kumar  (11 years ago)

case 1
b g b g b g b g
total number of ways of arrangement=8!
arrangement at odd positions=4!
arrangement at even positions=4!
so number of ways will be=8!/(4!*4!)=14
case 2
g b g b g b g b
total number of ways of arrangement=8!
arrangement at odd positions=4!
arrangement at even positions=4!
so number of ways will be=8!/(4!*4!)=14
so actual result will be=14+14=28 answer

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ABHIPSA MAYEE MAHARANA  (4 years ago)

First arrange the 4 boys in 4! Ways that is B_B_B_B
Now you can arrange the girls in 2 ways..
GBGBGBGB Or BGBGBGBG
According to que we have to select the 2nd way that is BGBGBGBG
so girls also arranged in 4! Ways
Therefore total number of ways=4!*4!=576

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