If n(A)=3 and n(B)=4 , then no. of of one-one function from A to B is :

Options

A. 12
B. 24
C. 36
D. none of these

Answer

To find the number of one-one functions from set A to set B, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of elements in sets A and B**:
- Given: \( n(A) = 3 \) and \( n(B) = 4 \).
- This means set A has 3 elements and set B has 4 elements.

2. **Understand the concept of one-one functions**:
- A function \( f: A \to B \) is called one-one (or injective) if different elements in A map to different elements in B. This means no two elements in A can map to the same element in B.

3. **Choose an element from B for each element in A**:
- For the first element in A, we can choose any of the 4 elements in B.
- For the second element in A, we can choose from the remaining 3 elements in B (since one has already been used).
- For the third element in A, we can choose from the remaining 2 elements in B.

4. **Calculate the total number of one-one functions**:
- The total number of one-one functions can be calculated by multiplying the number of choices for each element in A:
\[ \text{Total one-one functions} = n(B) \times (n(B) - 1) \times (n(B) - 2) \]
- Substituting the values:
\[ \text{Total one-one functions} = 4 \times 3 \times 2 \]

5. **Perform the multiplication**:
- Calculate \( 4 \times 3 = 12 \)
- Then calculate \( 12 \times 2 = 24 \)

6. **Conclusion**:
- Therefore, the total number of one-one functions from set A to set B is \( 24 \).

### Final Answer:
The number of one-one functions from A to B is **24**.