Find the number of ways in which 8 distinct toys can be distributed among 5 children.

Options

A. `5^(8)`
B. `8^(5)`
C. `3^(5)`
D. none of these

Explanation

To find the number of ways in which 8 distinct toys can be distributed among 5 children, we can follow these steps:

### Step 1: Understand the problem
We have 8 distinct toys and 5 distinct children. Each toy can be given to any one of the 5 children.

### Step 2: Determine the choices for each toy
For each toy, there are 5 choices (one for each child).

### Step 3: Calculate the total number of distributions
Since the toys are distinct, the choice for each toy is independent of the others. Therefore, for each of the 8 toys, we have 5 choices. This can be represented mathematically as:

\[ \text{Total ways} = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 = 5^8 \]

### Step 4: Compute \(5^8\)
Now we can calculate \(5^8\):

\[ 5^8 = 390625 \]

### Final Answer
Thus, the total number of ways to distribute the 8 distinct toys among 5 children is:

\[ \boxed{390625} \]

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