In how many ways can 5 prizes be given away to 4 boys when each boy is eligible for all the prizes ?

Options

A. a. 1024
B. b. 20
C. c. 625
D. d. 540

Answer

To solve the problem of distributing 5 prizes among 4 boys where each boy is eligible for all the prizes, we can follow these steps:

### Step 1: Understand the Problem
We have 5 distinct prizes and 4 distinct boys. Each prize can be given to any of the 4 boys.

### Step 2: Determine Choices for Each Prize
For each of the 5 prizes, we have 4 choices (one for each boy).

### Step 3: Calculate Total Combinations
Since the choice for each prize is independent of the others, we can use the multiplication principle. The total number of ways to distribute the prizes can be calculated as follows:
- For Prize 1: 4 choices (Boy 1, Boy 2, Boy 3, Boy 4)
- For Prize 2: 4 choices
- For Prize 3: 4 choices
- For Prize 4: 4 choices
- For Prize 5: 4 choices

Thus, the total number of ways to distribute the prizes is:
\[ 4 \times 4 \times 4 \times 4 \times 4 = 4^5 \]

### Step 4: Calculate \(4^5\)
Now we need to compute \(4^5\):
\[ 4^5 = 1024 \]

### Conclusion
Therefore, the total number of ways to distribute 5 prizes among 4 boys is **1024**.

---