there are red and blue balls which can be filled in 5 boxes. all balls are similar except color. what is the probability that no two consecutive boxes have blue balls.

• Ans: 12
  Exp/ A/q we hv sufficient no of R n B balls. We hv to focus only that no consecutive 2 balls having Blue ballls.
  Let we hv chose only ...1 B and 4 R balls...., So possible combinations are-
  (B,R,R,R,R), (R,B,R,R,R), (R,R,B,R,R), (R,R,R,B,R), (R,R,R,R,B). => 5ways
  Now assume we hv choose ....2 B and 3 R balls.., So possible combinations are-
  (B,R,B,R,R), (B,R,R,B,R), (B,R,R,R,B), (R,B,R,B,R), (R,B,R,R,B), (R,R,B,R,B) => 6ways
  (simply we r placing Blue balls at places 1-3,1-4,1-5,2-4,2-5, 3-5)
  
  similarly for 3 Blue balls, we hv only 1 option
  (B, R, B, R, B)...........................................................................................=> 1 ways
  we cant select 4 and 5 blue balls bcoz in these case we found 2 blue balls
  at consecutive place!!
  Total 5+6+1= 12 Ans.
• 9 years agoHelpfull: Yes(24) No(4)
• There are 5 spaces each can be filled by either blue or red so total no. of ways are2^5
  And no. of favourable outcomes are 12 hence
  12/2^5 or 3/8
• 9 years agoHelpfull: Yes(9) No(0)
• The question demands probability..not the number of ways. Could anyone of you please put some light on that?
  
• 9 years agoHelpfull: Yes(6) No(0)
• 13/32 is d ans
• 9 years agoHelpfull: Yes(5) No(0)
• let us find what is the prob. that two consecutive boxes have blue color
  5 boxes, TOTAL WAYS=2^5=32;
  consecutive boxes have blue color, total way= 23(simple permutation )
  so, prob. of consecutive boxes have blue color= 23/32;
  required probability= 9/32
• 9 years agoHelpfull: Yes(4) No(0)
• Possibilies 1.1 blue 4 red 2ND 2blue 3 red
  3Rd 3blue 2 red.
  For possibility 1St there are 5 ways as blue can be placed in any of 5 boxes
  For possibility 3Rd we have. 1 way only BRBRB
  For possibility 2ND
  If ist place is blue BR_ _ _ that is 3 options for 2nd blue ball
  If Ist place is red RBR_ _ that is two options for 2nd blue
  If Ist and 2nd place both red only possibility is RRBRB
  HENCE TOTAL NO OF WAYS =5+(3+2+1)+1=12
  
• 9 years agoHelpfull: Yes(2) No(2)
• Total no of ways filling 5 boxs with either blue or red balls 2^5=32
  Two adjacent boxes with blue 4 ways ie 12,23,34 and 45.
  Three adjacent boxes with blue 3ways ie 123,234,345.
  Four adjacent 1234,2345
  And 5 adjacent 1 way
  Hance total =(4+3+2+1)=10
  The no of ways of filling up the boxes such dt no 2 adjacent boxes hv blue =32-10=22
• 9 years agoHelpfull: Yes(2) No(0)
• ani is -3333
• 9 years agoHelpfull: Yes(1) No(0)