Ravish writes letters to his five friends and addresses the correspondig envelopes. The total number of ways in which letters can be placed in the envelopes so that at least two of them are in the wrong envelopes, is

Options

A. 120
B. 118
C. 119
D. 121

Explanation

To solve the problem of how many ways Ravish can place letters in envelopes such that at least two letters are in the wrong envelopes, we can use the concept of derangements. A derangement is a permutation of elements such that none of the elements appear in their original position.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to find the total number of arrangements of 5 letters in 5 envelopes such that at least 2 letters are in the wrong envelopes.

2. **Using the Complement Principle**:
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