There are 3 letters and 3 directed envelopes.

Question:

There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.

Solution:

Total number of ways in which the letters can be put = 3! = 6

Suppose, out of the three letters, one has been put in the correct envelope.

This can be done in 3C1, i.e. 3, ways.

Now, out of three, if two letters have been put in the correct envelope, then the last one has been put in the correct envelope as well.

This can be done in 3C3, i.e. one way.

∴ Number of ways = 3 + 1 = 4

∴ Number of ways in which no letter is put in the correct envelope = 6-">-4 = 2

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