If `n(A)=4,n(B)=3,n(AxxBxxC)=24`, then n(C ) equals

Options

A. 1
B. 2
C. 17
D. 288

Answer

To solve the problem step by step, we will use the information provided and apply the relevant formula.

### Step 1: Understand the Given Information
We are given:
- \( n(A) = 4 \) (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)

We need to find \( n(C) \) (the number of elements in set C).

### Step 2: Use the Formula for Cartesian Product
The formula for the number of elements in the Cartesian product of three sets A, B, and C is given by:
\[ n(A \times B \times C) = n(A) \times n(B) \times n(C) \]

### Step 3: Substitute the Known Values into the Formula
Now we can substitute the known values into the formula:
\[ 24 = n(A) \times n(B) \times n(C) \]
Substituting \( n(A) = 4 \) and \( n(B) = 3 \):
\[ 24 = 4 \times 3 \times n(C) \]

### Step 4: Calculate \( n(A) \times n(B) \)
Calculating \( 4 \times 3 \):
\[ 4 \times 3 = 12 \]
So, we have:
\[ 24 = 12 \times n(C) \]

### Step 5: Solve for \( n(C) \)
To find \( n(C) \), we divide both sides of the equation by 12:
\[ n(C) = \frac{24}{12} = 2 \]

### Conclusion
Thus, the number of elements in set C is:
\[ n(C) = 2 \]