If A and B are two sets such that n(A)=5 and n(B) = 6, then the number of one-one and onto mapping from A to B is

Options

A. 120
B. 720
C. 0
D. none of these

Answer

To find the number of one-one and onto mappings (bijective functions) from set A to set B, we need to consider the properties of these types of functions.

### Step-by-step solution:

1. **Understand the Definitions**:
- A function is **one-one** (injective) if different elements in set A map to different elements in set B.
- A function is **onto** (surjective) if every element in set B is mapped by at least one element in set A.

2. **Check the Cardinalities**:
- Given that \( n(A) = 5 \) and \( n(B) = 6 \), we note that the number of elements in set A is less than the number of elements in set B.

3. **Determine the Possibility of One-One and Onto Mapping**:
- For a function to be both one-one and onto, the number of elements in both sets must be equal. Since \( n(A) < n(B) \), it is impossible to have a one-one and onto mapping from A to B.

4. **Conclusion**:
- Therefore, the number of one-one and onto mappings from set A to set B is **0**.

### Final Answer:
The number of one-one and onto mappings from A to B is **0**.