There are 4 different monitors and 6 different mother boards. How many different arrangements can be made to purchase a monitor and a motherboard?

Options

A. 12
B. 24
C. 18
D. `6^4`

Answer

To solve the problem of how many different arrangements can be made to purchase a monitor and a motherboard, we can follow these steps:

### Step 1: Identify the number of choices for monitors and motherboards
We have:
- 4 different monitors (let's label them as M1, M2, M3, M4)
- 6 different motherboards (let's label them as MB1, MB2, MB3, MB4, MB5, MB6)

### Step 2: Determine the combinations
For each monitor, we can pair it with any of the 6 motherboards. This means:
- For Monitor M1, we can choose from 6 motherboards.
- For Monitor M2, we can also choose from 6 motherboards.
- The same applies to M3 and M4.

### Step 3: Calculate the total arrangements
Since the choice of motherboard is independent for each monitor, we can multiply the number of choices:
- Total arrangements = Number of monitors × Number of motherboards
- Total arrangements = 4 monitors × 6 motherboards = 24 arrangements

### Conclusion
Thus, the total number of different arrangements to purchase a monitor and a motherboard is **24**.