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:
- 5
- 3
- 1
- 2
Hint:
First we will find the total number of ways of putting letters in the envelope, then we will find the number of ways of putting 1 letter, 2 letters and 3 letters in the right envelope respectively. At last, to find the total no, of ways when no letter will be in the right envelope we will subtract the number of ways of putting 1 letter, 2 letters and 3 letters in the right envelope respectively from total number of ways.
The correct answer is: 2
Total number ways in which 3 letters can be put in 3 different envelopes= 3! = 6
now, numbers of ways when only 1 letter is put in the right envelope = 
=3
number of ways when 2 letters are put in the right envelope = 0
as when we put 2 letters in the right envelope the third letter would be automatically in the right envelope
number of ways when 3 letters are put in the right envelope = 1
So, the no. of ways when no letter will be in the right envelope=6-(3+0+1) =6-4 =2
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