Home
Class 12
MATHS
There are n letters and n addressed e...

There are `n` letters and `n` addressed envelopes. Find the probability that all the letters are not kept in the right envelope.

Text Solution

Verified by Experts

The correct Answer is:
`1 - (1)/(n!)`

Required probability is 1 - P(all letters in right envelope) = 1 - 1/n!
(As there are total number of n! ways in which letters can take envelopes and just one way in which they have corresponding envelopes.)
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY I

    CENGAGE ENGLISH|Exercise Exercise 9.3|7 Videos
  • PROBABILITY I

    CENGAGE ENGLISH|Exercise MCQ|54 Videos
  • PROBABILITY I

    CENGAGE ENGLISH|Exercise Exercise 9.1|6 Videos
  • PROBABILITY

    CENGAGE ENGLISH|Exercise Comprehension|2 Videos
  • PROBABILITY II

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

Similar Questions

Explore conceptually related problems

There are 4 letters and 4 addressed envelopes. Find the probability that all the letters are not dispatched in right envelopes.

There are 6 letters and 6 addressed envelopes. Find the probability that at least one letter goes into the wrong envelope.

There are n letters and n addressed envelopes . If the letters are placed in the envelopes at random , what is the probability that all the letters are not placed in the right evelope ?

Three letters, to each of which corresponds an envelope, are placed in the envelopes at random. The probability that all the letters are not placed in the right envelopes, is

A person write 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is a. 1/4 b. 11/24 c. 15/24 d. 23/24

A person write 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is a. 1/4 b. 11/24 c. 15/24 d. 23/24

There are four letters and four directed envelopes. The number of ways in which all the letters can be put in the wrong envelope is a. 8 b. 9 c. 16 d. none of these

Three letters are written to different persons , and the addresses on the three envelopes are also written . Without looking at the addresses , find the probability that the letters go into the right envelopes .

Two letters are drawn from the english alphabets. Find the probability that both letters are vowels.

Ravi writes 5 letters and addresses 5 envelopes. If the letters are placed in the envelopes at random, then the probability that a least one letter goes into the wrong envelope is

CENGAGE ENGLISH-PROBABILITY I -Exercise 9.2
  1. If two fair dices are thrown and digits on dices are a and b, then fin...

    Text Solution

    |

  2. There are n letters and n addressed envelopes. Find the probability...

    Text Solution

    |

  3. Find the probability of getting total of 5 or 6 in a single throw o...

    Text Solution

    |

  4. Two integers are chosen at random and multiplied. Find the probabil...

    Text Solution

    |

  5. If out of 20 consecutive whole numbers two are chosen at random, th...

    Text Solution

    |

  6. A bag contains 3 red, 7 white, and 4 black balls. If three balls ar...

    Text Solution

    |

  7. An ordinary cube has 4 blank faces, one face mark 2 and another marke...

    Text Solution

    |

  8. If the letters of the word REGULATIONS be arranged at random, find ...

    Text Solution

    |

  9. A five-digit number is formed by the digit 1, 2, 3, 4, 5 without repet...

    Text Solution

    |

  10. Five persons entered the lift cabin on the ground floor of an 8-flo...

    Text Solution

    |

  11. Two friends Aa n dB have equal number of daughters. There are three ci...

    Text Solution

    |

  12. about to only mathematics

    Text Solution

    |

  13. There are eight girls among whom two are sisters, all of them are to s...

    Text Solution

    |

  14. A bag contains 50 tickets numbered 1, 2, 3, .., 50 of which five are ...

    Text Solution

    |

  15. A pack of 52 cards is divided at random into two equals parts. Find th...

    Text Solution

    |

  16. If a digit is chosen at random from the digits 1,\ 2,\ 3,\ 4,\ 5,\ 6...

    Text Solution

    |

  17. If two distinct numbers m and n are chosen at random form the set {1, ...

    Text Solution

    |

  18. Two number aa n db aer chosen at random from the set of first 30 natur...

    Text Solution

    |

  19. Twelve balls are distributed among three boxes, find the probability ...

    Text Solution

    |