How many methods are possible for arranging 5 boys and 4 girls in such a way that no 2 girls could sit together?

• Solution given by site administrator for same puzzle ( earlier) was not correct.
  
  The arrangement can be done as below
  X..B..X..B...X..B...X..B...X..B..X
  
  where b is the position of Boys and 4 girls can be placed at any of 6 positions marked as X.
  
  so Number of arrangements will be
  
  5! * 6p4 = 120*360 = 43200
• 13 years agoHelpfull: Yes(12) No(2)
• Number of methods will be
  
  5! * 6p4
  
  as 4 girls can be placed at the locations marked by X in
  
  XBXBXBXBXBX
  
  120*6*5*4*3=120*360
• 13 years agoHelpfull: Yes(5) No(0)
• 5!*6!/(6-4)!=5!*6!/2=120*720/2=43200
• 13 years agoHelpfull: Yes(4) No(2)
• 5 boys In 5 places so 5 chances
  in between boys and around them total 6 places in that 6 places yo6p4
  u need to select 4 girls and arrange them in 4 places for that we need permutation so 6p4
  so ans is 5*6p4
  x b x b x b x b x b x
• 8 years agoHelpfull: Yes(3) No(0)
• _B_B_B_B_B_
  no of ways for arranging 5 boys =5!
  no of ways for arranging 4 girls=7c4*4!
  so total ways of arranging 5 boys and 4 girls under above condition=5!*7c4*4!=100800
• 13 years agoHelpfull: Yes(2) No(6)
• boys can be arrranged in 5! and girls in 6P4 so final sol is 5!*6P4
• 7 years agoHelpfull: Yes(1) No(0)
• Answer: 359280
  Total no of method for arranging the 9 people(5B+4G)=9P9.
  Divide the four girls in two group where each group having two girls.
  Now....we have the situation like the following.....
  ___B___B___B___B__B___
  means we have 6 blank space in which we have to select 2 for two groups.and further more these group member can be arrange 2P2 ways.
  So total number for arranging 9 people in which two girls sitting together is 5P5*(6C2*2P2)
  
  Now total number of method for arranging the 5B and 4G such that NO 2 girls could sit together are:
  9P9 - 5P5*(6C2*2P2)=359280
• 8 years agoHelpfull: Yes(0) No(2)
• girls in 4! ways and boys 3! ways
  therefore 4*4!*5!=576
• 8 years agoHelpfull: Yes(0) No(2)
• 5!*4!/2!=360
  
• 7 years agoHelpfull: Yes(0) No(2)
• there are 5 boys and place where girls can sit 6 so,
  5!*6p4= 43200
• 7 years agoHelpfull: Yes(0) No(0)
• 5!*6!/(6-4)!=5!*6!/2=120*720/2=43200
• 6 years agoHelpfull: Yes(0) No(0)
• 4 may be correct
• 4 years agoHelpfull: Yes(0) No(0)