If `n(A)=4,n(B)=3" and "n(AxxBxxC)=24`, then n(C) is equal to

Options

A. 288
B. 1
C. 12
D. 2

Explanation

To solve the problem, we need to find the number of elements in set C, given the following information:

- \( n(A) = 4 \) (the number of elements in set A)
- \( n(B) = 3 \) (the number of elements in set B)
- \( n(A \times B \times C) = 24 \) (the number of elements in the Cartesian product of sets A, B, and C)

### Step-by-Step Solution:

1. **Understanding the Cartesian Product**:
The number of elements in the Cartesian product of three sets \( A \), \( B \), and \( C \) can be calculated using the formula:
\[ n(A \times B \times C) = n(A) \times n(B) \times n(C) \]

2. **Substituting Known Values**:
We know:
- \( n(A) = 4 \)
- \( n(B) = 3 \)
- \( n(A \times B \times C) = 24 \)

Plugging these values into the formula gives us:
\[ 24 = 4 \times 3 \times n(C) \]

3. **Calculating \( n(C) \)**:
First, calculate \( 4 \times 3 \):
\[ 4 \times 3 = 12 \]
Now, substitute this back into the equation:
\[ 24 = 12 \times n(C) \]

4. **Isolating \( n(C) \)**:
To find \( n(C) \), divide both sides of the equation by 12:
\[ n(C) = \frac{24}{12} = 2 \]

5. **Conclusion**:
Therefore, the number of elements in set C is:
\[ n(C) = 2 \]

### Final Answer:
The number of elements in set C is \( 2 \).

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