You have Rs.2 with u.You have to play a game in which if u win u will get 1 Re. and if lost you will lose 1 Re.You can lose up to 3 times. But if u get 5 Rs, you are left out of the game. In how many ways is this possible?

• case 1: I win every game
  WWW =1
  he has three rupees
  case 2: I lose 1 game
  so the number of combination will be 4
  LWWWW, WLWWW, WWLWW, WWWLW
  case 3: I lose 2 games
  combinations will be 15
  LLWWWWW, WLLWWWW, WWLLWWW, WWWLLWW, WWWWLLW, LWLWWWW, LWWLWWW, LWWWLWW,
  LWWWWLW, WLWLWWW, WLWWLWW, WLWWWLW, WWLWLWW, WWLWWLW, WWWLWL
  case 3:I lose 3 games
  so combination will be
  LLLWWWWWW, WLLLWWWWW, WWLLLWWWW, WWWLLLWWW, WWWWLLLWW, WWWWWLLLW
  LLWLWWWWW, LLWWLWWWW, LLWWWLWWW, LLWWWWLWW, LLWWWWWLW
  WLLWLWWWW, WLLWWLWWW, WLLWWWLWW, WLLWWWWLW, WWLLWLWWW, WWLLWWLWW
  WWLLWWWLW, WWWLLWLWW, WWWLLWWLW, WWWWLLWLW, LWLLWWWWW, LWWLLWWWW
  LWWWLLWWW, LWWWWLLWW, LWWWWWLLW, WLWLLWWWW, WLWWLLWWW, WLWWWLLWW
  WLWWWWLLW, WWLWLLWWW, WWLWWLLWW, WWLWWWLLW, WWWLWLLWW, WWWWLWLLW
  LWLWLWWWW, LWLWWLWWW, LWLWWWLWW, LWLWWWWLW, WLWLWLWWW, WLWLWWLWW
  WLWLWWWLW, WWLWLWLWW, WWLWLWWLW, WWWLWLWLW
  SO total of 40 combination is possible if I loose 3 games
  so total number of ways in which i will win rs 5 and leave the game is
  1+4+15+46=66
  
  
  
• 10 years agoHelpfull: Yes(20) No(18)
• already Rs.2
  2+(3 win) ----> 1 way
  Maximum 3 loss
  2+(6 win)(- 3 loss) : 9!/6!*3!
  2+(5 win)(-2 loss) : 7!/5!*2!
  2+(4 win)(-1 loss) : 5!/4!*1!
  
  1+(9!/6!*3!)+(7!/5!*2!)+(5!/4!*1!)= 111
• 10 years agoHelpfull: Yes(9) No(5)
• @ SHABIH ABBAS in case 2 and 3 after 3 wins www the person will be out of the game so many combinations (in case 2 and 3) which you have given will not come.
• 10 years agoHelpfull: Yes(5) No(1)
• ans is 66 ways.
  
• 10 years agoHelpfull: Yes(1) No(33)
• ans is 76
  for combination WWW-1
  for combination WLWWW->4!/3!=4
  for combination WLLWWWW->6!/(4!*2!)=15
  for combination WLLLWWWWW->7!/(3!*5!)=56
  TOTAL=56+15+4+1=76
• 10 years agoHelpfull: Yes(1) No(1)
• Now the logic of the Question is in this that he can be out of the game as soon as he gets 5 Rs and a maximum of 3 loses are allowed
  
  for 0 lose
  we have number of ways until he gets point 5 and is out of the game as 3!/3!=1
  
  for 1 lose
  number of ways are =4!/3!=4
  
  for 2 lose it is
  number of ways are =6!/4!=15
  
  for 3 lose it is
  number of ways are =46
  
  so total ways are 1+46+15+4=66
  
• 9 years agoHelpfull: Yes(1) No(0)
• plzz explain
• 10 years agoHelpfull: Yes(0) No(2)
• can anyone xplain plz???
• 10 years agoHelpfull: Yes(0) No(1)
• can anyone expalin it .??
• 10 years agoHelpfull: Yes(0) No(3)
• plz explain this
• 10 years agoHelpfull: Yes(0) No(2)
• can any one explain it
  
• 10 years agoHelpfull: Yes(0) No(1)
• plz explain
  
• 10 years agoHelpfull: Yes(0) No(0)
• case 1: lwlwl
  case 2: wwlll
  case 3: wllwl
  case 4: llwwl
  case 5: lwwll
  so in 5 ways
• 10 years agoHelpfull: Yes(0) No(4)
• please explain the sum?
• 10 years agoHelpfull: Yes(0) No(0)
• Now the logic of the Question is in this that he can be out of the game as soon as he gets 5 Rs and a maximum of 3 loses are allowed
  
  for 0 lose
  we have number of ways until he gets point 5 and is out of the game as 3!/3!=1
  
  for 1 lose
  number of ways are =4!/3!=4
  
  for 2 lose it is
  number of ways are =6!/4!=15
  
  for 3 lose it is
  number of ways are =46
  
  so total ways are 1+46+15+4=66
  
• 9 years agoHelpfull: Yes(0) No(0)
• 91ways...
  1+6p1+7p2+(7p2*1)=91 ways
• 9 years agoHelpfull: Yes(0) No(0)