A boy has Rs 2. He wins or loses Re 1 at a time If he wins he gets Re 1 and if he loses the game he loses Re 1.He can loose only 5 times. He is out of the game if he earns Rs 5.Find the number of ways in which this is possible?

• 16 ways are possible.
• 13 years agoHelpfull: Yes(22) No(19)
• He has 2Rs.He wins or loses Re 1 at a time.
  for 1Rs.He may have different probabilities as (WW,WL,LW,LL)i.e,for one rupee he has 8chances in the same way for another one rupee he has another 8 chances .
  So,total number of chances/ways are 16.
  /*If he looses 4times one rupee will be lossed and if he had another loss he is out of game*/
• 11 years agoHelpfull: Yes(22) No(6)
• how dipin???
  pls xplain....
• 13 years agoHelpfull: Yes(12) No(3)
• no lose ( 1 way)
  one lose + four wins(3 ways)
  twoloses+5 wins(7 ways)
  three loses+6 wins( 21 ways)
  four loses+ 7 wins(49 ways)
  five loses he is out of the game
  total ways = 1+3+7+21+49 = 81
• 9 years agoHelpfull: Yes(0) No(10)
• Dipin Plz explain
• 8 years agoHelpfull: Yes(0) No(0)
• please explain the answer in detail
• 8 years agoHelpfull: Yes(0) No(0)
• 0L -> 1 way
  1L -> 3 ways
  2L -> 7 ways
  3L -> 4 ways
  4L -> 1 way
  total 16 ways
• 8 years agoHelpfull: Yes(0) No(1)
• Let's analyze the situation step by step to find the number of ways in which the boy can reach the condition of earning Rs. 5.
  
  Let's represent the boy's winnings and losses as follows:
  
  W = Rs. 1 (When he wins)
  
  L = Rs. -1 (When he loses)
  
  Since he can lose only 5 times and is out of the game after earning Rs. 5, we can consider different scenarios where he wins and loses.
  
  1. If he wins 5 times in a row (WWWWW), he will earn: 5W = Rs. 5 (He's out of the game)
  
  2. If he wins 4 times and then loses once (WWWWL), he will earn: 4W + 1L = Rs. 3
  
  3. If he wins 3 times and then loses twice (WWWLL), he will earn: 3W + 2L = Rs. 1
  
  4. If he wins 2 times and then loses three times (WWLLL), he will earn: 2W + 3L = Rs. -1
  
  5. If he wins once and then loses four times (WLLLL), he will earn: 1W + 4L = Rs. -3
  
  6. If he loses five times in a row (LLLLL), he will earn: 5L = Rs. -5 (He's out of the game)
  
  Now, let's count the number of ways for each scenario:
  
  1. WWWWW: Only one way
  
  2. WWWWL: Number of ways to arrange 4W and 1L = 5! / (4! * 1!) = 5
  
  3. WWWLL: Number of ways to arrange 3W and 2L = 5! / (3! * 2!) = 10
  
  4. WWLLL: Number of ways to arrange 2W and 3L = 5! / (2! * 3!) = 10
  
  5. WLLLL: Number of ways to arrange 1W and 4L = 5! / (1! * 4!) = 5
  
  6. LLLLL: Only one way
  
  Now, sum up the number of ways for each scenario:
  
  Total number of ways = 1 + 5 + 10 + 10 + 5 + 1 = 32
  
  So, there are 32 ways in which the boy can reach the condition of earning Rs. 5 before being out of the game.
• 7 Months agoHelpfull: Yes(0) No(0)
• Let's analyze the situation step by step to find the number of ways in which the boy can reach the condition of earning Rs. 5.
  
  Let's represent the boy's winnings and losses as follows:
  
  W = Rs. 1 (When he wins)
  
  L = Rs. -1 (When he loses)
  
  Since he can lose only 5 times and is out of the game after earning Rs. 5, we can consider different scenarios where he wins and loses.
  
  1. If he wins 5 times in a row (WWWWW), he will earn: 5W = Rs. 5 (He's out of the game)
  
  2. If he wins 4 times and then loses once (WWWWL), he will earn: 4W + 1L = Rs. 3
  
  3. If he wins 3 times and then loses twice (WWWLL), he will earn: 3W + 2L = Rs. 1
  
  4. If he wins 2 times and then loses three times (WWLLL), he will earn: 2W + 3L = Rs. -1
  
  5. If he wins once and then loses four times (WLLLL), he will earn: 1W + 4L = Rs. -3
  
  6. If he loses five times in a row (LLLLL), he will earn: 5L = Rs. -5 (He's out of the game)
  
  Now, let's count the number of ways for each scenario:
  
  1. WWWWW: Only one way
  
  2. WWWWL: Number of ways to arrange 4W and 1L = 5! / (4! * 1!) = 5
  
  3. WWWLL: Number of ways to arrange 3W and 2L = 5! / (3! * 2!) = 10
  
  4. WWLLL: Number of ways to arrange 2W and 3L = 5! / (2! * 3!) = 10
  
  5. WLLLL: Number of ways to arrange 1W and 4L = 5! / (1! * 4!) = 5
  
  6. LLLLL: Only one way
  
  Now, sum up the number of ways for each scenario:
  
  Total number of ways = 1 + 5 + 10 + 10 + 5 + 1 = 32
  
  So, there are 32 ways in which the boy can reach the condition of earning Rs. 5 before being out of the game.
• 6 Months agoHelpfull: Yes(0) No(0)