Question
The number of ways in which four letters can put in four addressed envelopes so that no letter goes into the envelope meant for it is :
- 7
- 9
- 4
- 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, 3 letters and 4 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, 3 letters and 4 letters in the right envelope respectively from total number of ways.
The correct answer is: 9
Total number of ways of putting 4 letters in 4 envelopes = 4! =24
Now, number of ways of putting only 1 letter in the right envelope= 
=8
number of ways of putting only 2 letters in the right envelopes =
=6
number of ways of putting 3 letters in the right envelope= 0, as when we will put three letters in the right envelope the last will automatically go in the right place.
number of ways of putting 4 letters in the right envelope= 1
So, the number of ways in which four letters can put in four addressed envelopes so that no letter goes into the envelope meant for it =24-(8+6+0+1)=24-15=9
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