First slide

Combinations

Question

There are 3 letters and 3 addressed envelopes corresponding to them. The number of ways in which the letters be placed in the envelopes so that no letter is in the right envelope is

Easy

A

5
B

3
C

1
D

2

Solution

The number of ways in which the letters be placed in the envelopes so that no letter is in the right envelope is =
$3! [1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!}] = 2$ $(D e r a n g e m e n t f o r m u l a = n! [1 - \frac{1}{1!} + \frac{1}{2!} - \frac{1}{3!} + . . . . . . . + {(- 1)}^{n} \frac{1}{n!}])$

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