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)?

• 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
  
• 11 years agoHelpfull: Yes(24) No(1)
• - 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
• 11 years agoHelpfull: Yes(5) No(4)
• 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
• 11 years agoHelpfull: Yes(3) No(14)
• 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
• 10 years agoHelpfull: Yes(1) No(0)
• 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
  
• 11 years agoHelpfull: Yes(0) No(4)
• 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
• 11 years agoHelpfull: Yes(0) No(0)
• 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
• 4 years agoHelpfull: Yes(0) No(0)