In how many ways , 5 different chocolate can put in 5 identical boxes ,such that one box can contains only one chocolate.

Options

A. 14400
B. 720
C. 72
D. 120

Answer

To solve the problem of how many ways 5 different chocolates can be put in 5 identical boxes, where each box can contain only one chocolate, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We have 5 different chocolates (let's label them as A, B, C, D, and E) and 5 identical boxes. Each box can only hold one chocolate. Since the boxes are identical, the arrangement of chocolates in the boxes does not depend on which box is used, only on which chocolates are placed together.

2. **Identifying the Arrangement**: Since each chocolate must go into a box and there are no restrictions on how many boxes can be used (other than the fact that each box can only hold one chocolate), we can think of this as a permutation problem where we are arranging 5 distinct items.

3. **Calculating the Number of Ways**: The number of ways to arrange n distinct items is given by n!. In our case, we have 5 distinct chocolates, so we calculate:
\[ 5! = 5 \times 4 \times 3 \times 2 \times 1 \]

4. **Performing the Calculation**:
- Calculate \(5! = 120\).

5. **Conclusion**: Since the boxes are identical, the arrangement of chocolates in the boxes does not change the outcome, and thus the total number of ways to distribute the chocolates into the boxes is simply \(120\).

### Final Answer:
The total number of ways to put 5 different chocolates into 5 identical boxes is **120**.

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