There are unlimited number of identical balls of four different colours. How many arrangements of at most 8 balls in row can be made by using them?

Options

A. 21845
B. 87380
C. 262140
D. none of these

Explanation

To solve the problem of how many arrangements of at most 8 balls in a row can be made using an unlimited number of identical balls of four different colors, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We have four different colors of identical balls and we can use at most 8 balls in a row. We need to find the total number of arrangements possible with these constraints.

2. **Calculating Arrangements for Each Case**:
- **1 Ball**: For 1 ball, we can choose any of the 4 colors. So, the number of arrangements is \(4^1 = 4\).
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