The number of ways in which 5 distinct toys can be distributed among 8 children is

Options

A. `2^(15)`
B. `8^(5)`
C. `5^(8)`
D. `32768`

Answer

To solve the problem of distributing 5 distinct toys among 8 children, we can follow these steps:

### Step-by-step Solution:

1. **Identify the number of toys and children**:
- We have 5 distinct toys (let's denote them as T1, T2, T3, T4, T5).
- We have 8 distinct children (let's denote them as C1, C2, C3, C4, C5, C6, C7, C8).

2. **Determine the distribution options for each toy**:
- For each toy, we can choose any one of the 8 children to give the toy to.
- This means that for the first toy (T1), there are 8 possible choices (C1 to C8).
- The same applies for the second toy (T2), third toy (T3), fourth toy (T4), and fifth toy (T5).

3. **Calculate the total number of ways to distribute the toys**:
- Since each toy can be given to any of the 8 children independently, we multiply the number of choices for each toy.
- Therefore, the total number of ways to distribute the toys is:
\[ \text{Total ways} = 8 \times 8 \times 8 \times 8 \times 8 = 8^5 \]

4. **Final calculation**:
- We can compute \(8^5\):
\[ 8^5 = 32768 \]

5. **Conclusion**:
- The number of ways in which 5 distinct toys can be distributed among 8 children is \(8^5\) or 32768.