The Wrong Letters

Probability Level 2

There are 4 letters which correspond to 4 different people. Then what is the probability that none of the letter is given to the right person?

7/12 4/5 2/3 3/8

Ameya Mishra by Ameya Mishra , 17, India

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1 solution

Ameya Mishra
Jan 23, 2018
  • Using the derangement permutations,
  • where n= number of people.
  • derangement permutation=n!(1/2! - 1/3! + 1/4! - 1/5! ......... +1/n!)
  • therefore the number of cases in which the letter does not go to the right person,
  • 4!(1/2! - 1/3! + 1/4!)
  • =24*9/24
  • =9
  • Number of derangements =9
  • therefore probability of the letter not going to the right person=>9/24=3/8(answer)
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