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If n things are arranged in a row, the number of way in which they can be arranged so that non occupies its original position is `n!(1-(1)/(1!)+(1)/(2!)-(1)/(3!)+* * * + (-1)^(n)(1)/(n!))`
The number of ways of putting 6 letters into 6 addressed envelopes so that exactly 2 letters are in wrong is

A

`""^(6)C_(4)`

B

30

C

45

D

28

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A
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Knowledge Check

  • If n things are arranged in a row, the number of way in which they can be arranged so that non occupies its original position is n!(1-(1)/(1!)+(1)/(2!)-(1)/(3!)+* * * + (-1)^(n)(1)/(n!)) The number of ways of putting at least 3 out of 6 letters in wrong envelops is

    A
    265
    B
    40
    C
    704
    D
    50

  • If n things are arranged in a row, the number of way in which they can be arranged so that non occupies its original position is n!(1-(1)/(1!)+(1)/(2!)-(1)/(3!)+* * * + (-1)^(n)(1)/(n!)) Five boys are to be seated in a row. The number of ways in which 3 boys are not seated in the place specfied to them is

    A
    `""^(5)P_(2)`
    B
    10
    C
    40
    D
    25

  • Find the number of ways in which all the 6 different letters are placed in 6 addressed envelops so that all the letters are in the wrong envelops.

    A
    554
    B
    618
    C
    620
    D
    None of these

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