Question

There are 5 letters and 5 directed envelopes. Find the number of ways in which the letters can be put into the envelopes so that all are not put in directed envelopes.

• A. 129
• B. 119
• C. 109
• D. 139
• E. None of these

Answer 1

The correct option is B 119

Here, the first letter can be in any 1 of the 5 envelopes in 5 ways. Second letter can be put in any 1 of the 4 remaining envelopes in 4 ways. Continuing in this way, we get the total number of ways in which 5 letters can be put into 5 envelopes $=5\times 4\times 3\times 2\times 1=120.$ Since out of the 120 ways, there is 1 one way for putting each letter in the correct envelope. Hence, the number of ways of putting letters all not in directed envelopes $=120-1=119ways.$