In a steamer there are stalls for 12 animals and there are cows, horses and calves (not less than 12 of each) ready to be shipped, the total number of ways in which the shipload can be made, is

Options

A. `""_(12)C_(3)`
B. `""_(12)P_(3)`
C. `3^(12)`
D. `12^(3)`

Answer

To solve the problem of arranging 12 animals (cows, horses, and calves) in 12 stalls on a steamer, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We have 12 stalls and we need to fill these stalls with animals. The types of animals available are cows, horses, and calves. Each stall can contain one animal, and we have at least 12 of each type of animal.

2. **Choices for Each Stall**: For each stall, we have three choices of animals: we can place either a cow, a horse, or a calf.

3. **Calculating the Total Choices**: Since there are 12 stalls and each stall can independently have one of the three types of animals, we can calculate the total number of arrangements by considering the choices for each stall.

4. **Using the Multiplication Principle**: The total number of ways to fill the stalls can be calculated using the multiplication principle of counting. Since each stall has 3 choices, and there are 12 stalls, the total number of ways to arrange the animals is:
\[ \text{Total Ways} = 3 \times 3 \times 3 \times \ldots \text{(12 times)} = 3^{12} \]

5. **Final Calculation**: Now we compute \(3^{12}\):
\[ 3^{12} = 531441 \]

Thus, the total number of ways in which the shipload can be made is **531441**.