Four letters are to be placed in four addressed envelopes. If the letters are placed at random into the envelopes, find out the following probabilities.

The probability that none of the letters are placed in the right envelopes is:

a) 1/24

b) 3/8

c) 23/24

d) 13/24

e) None of the above

• the ans is: 3/8
  
  Total no. of ways to put the letters in the envelop is !4= 24
  
  all letters are wrongly placed..
  suppose the letters are 1,2,3,4
  if i write 1234 its mean in envelop 1 there is 1st letter, in 2 there is 2nd..so on
  
  there would be 9 such combination to put the letters in the wrong envelop:
  2143, 2341, 2413
  3142, 3412, 3421
  4123, 4312, 4321
  
  so 9/24= 3/8 :)
• 12 years agoHelpfull: Yes(10) No(5)
• Ans: 3/8
  Soln: for n letters not placed in correct envelope = (1/2!)-(1/3!)+(1/4!)-...+(1/n!)
  so for 4 letters ans is 3/8...
• 12 years agoHelpfull: Yes(5) No(5)
• This Is The Case Of Dearrangement...So None Are Placed Is (1/2!)-(1/3!)+(1/4!)=3/8
• 12 years agoHelpfull: Yes(4) No(4)
• ans..c)
  total no. of case n(s)=4!=24
  no of enent n(e)=1
  probability of placing letters in right envelope=n(e)/n(s)=1/24
  so,...probability of not placing =(1-1/24)=23/24
  
• 12 years agoHelpfull: Yes(3) No(12)