A person writes letters to $6$ friends and addresses the corresponding envelopes. The number of ways in which $5$ letters can be placed in wrong envelopes is

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Solution

The number of ways in which all the $5$ letters be placed in wrong envelopes
$=^{6} C_{5} \cdot 5! (\frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \frac{1}{5!})$
$= 720 (\frac{1}{2} - \frac{1}{6} + \frac{1}{24} - \frac{1}{120}) = 264$

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Standard XII Mathematics

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A person writes letters to 6 friends and addresses the corresponding envelopes. The number of ways in which 5 letters can be placed in wrong envelopes is

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A person writes letters to $6$ friends and addresses the corresponding envelopes. The number of ways in which $5$ letters can be placed in wrong envelopes is

The number of ways in which all the $5$ letters be placed in wrong envelopes
$=^{6} C_{5} \cdot 5! (\frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \frac{1}{5!})$
$= 720 (\frac{1}{2} - \frac{1}{6} + \frac{1}{24} - \frac{1}{120}) = 264$