There are 5 envelopes corresponding to 5 letters.If the letters are placed in the envelopes at random,what is the probability that no single letter is placed in the right envelope?

• this is the disarrangement problem.. so no of ways all 5 letter will go in wrong place= 5!*[1/2!-1/3!+1/4!-1/5!]=60-20+5-1=44. total case= 5!=120.
  so probability that no one is in right envelope=44/120
• 9 years agoHelpfull: Yes(55) No(8)
• 119/120
  5 letters are placed in 5 eneveopes in 5! ways
  all letters are in correct envelopes prob. 1/5!
  so prob. of not in correct enevelpoe 1-1/5!
• 9 years agoHelpfull: Yes(9) No(16)
• total possibilities= 5!
  only one can be correct out of these 5!
  so the required probability will be (5!-1)/5!=119/120
• 9 years agoHelpfull: Yes(5) No(7)
• ans. should be 0.
• 9 years agoHelpfull: Yes(4) No(28)
• ans.44/120
• 9 years agoHelpfull: Yes(3) No(6)
• no of ways=5!=120
  only one arrangement is right position.
  so probability for right position is 1/120(for one letter)
  probability for 5 letter is 5/120=1/24
  so probability for wrong place=1-1/24=23/24
• 9 years agoHelpfull: Yes(3) No(3)
• 5 envelopes corresponding to 5 letters i.e in an random way possible combinations is 5c5,
  the possibility of all letters is placed in right envelope is 5c5
  one thing we have to remember in probability is p(s)=1 (ALWAYS)
  that y the possibility for not getting even single letter can be given as
  (p(s)-getting all letter placed in right envelope)
  =1-5c5
  =1-1
  =0
• 9 years agoHelpfull: Yes(2) No(9)
• 4*3*2/120=
  1/5.....
• 9 years agoHelpfull: Yes(2) No(5)
• ans is 119/120
  
• 9 years agoHelpfull: Yes(1) No(4)
• Answer is 0
  
  because... probability that all letter is placed in right envelpo = 5C5
  now probability that none of the lettr is placed in the right envelop= 1- 5C5 = 1-1= 0
• 9 years agoHelpfull: Yes(1) No(2)
• The total number of solution of disarrangement problem can be solved as :
  No of letters(n) = 5
  D(n)=n![1/1!-1/2!+1/3!-1/4!+.....(-1)n /n!]
  W=n!
  solution=D(n)/W
• 7 years agoHelpfull: Yes(1) No(1)
• there is only one way to place in the right envelope
  but 5 lettrers are placed in 5 envelopes in 5!ways
  so probability of not in correct enevelope is 5! -1=119
  
• 9 years agoHelpfull: Yes(0) No(3)
• prob for going in correct envelope :- 1/5
  so for going in wrong envelope :- 1-1/5= 4/5
• 9 years agoHelpfull: Yes(0) No(6)
• how 19????????/
  
• 9 years agoHelpfull: Yes(0) No(1)
• Answer is zero as it is impossible to put all letters wrong
  
• 9 years agoHelpfull: Yes(0) No(7)
• 4*4*4*4*4=1024
  bcz except fixed one others 4 çan put for every 5.
• 9 years agoHelpfull: Yes(0) No(1)
• it's a question of dearrangement .ans = 26 .
• 6 years agoHelpfull: Yes(0) No(1)
• e are 5 letters and five addressed envelopes. the number of ways in which all the letters can be put in wrong envelopes is
  
  Total Number of ways = 5! = 120
  
  The formula for the derangement can be used directly. The number of derangements is
  
  n! (1/2!−1/3!+1/4!+…+(−1)ⁿ/n!)
  
  Here n = 5
  
  5 ! ( 1/2! - 1/3! + 1/4! - 1/5!)
  
  = 120 ( 1/2 - 1/6 + 1/24 - 1/120)
  
  = 60 - 20 + 5 - 1
  
  = 65 - 21
  
  = 44
  So probabilty = 44/120
• 5 years agoHelpfull: Yes(0) No(0)