If the set `A` contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is `720` (b) 120 (c) 0 (d) none of these

Options

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

Explanation

To solve the problem of finding the number of one-one and onto mappings (bijective functions) from set A to set B, we can follow these steps:

### Step 1: Understand the Definitions
A function is one-one (injective) if different elements in the domain map to different elements in the codomain. A function is onto (surjective) if every element in the codomain has at least one element from the domain mapping to it. A function that is both one-one and onto is called a bijection.

### Step 2: Analyze the Given Sets
We are given:
- Set A has 5 elements.
- Set B has 6 elements.

### Step 3: Determine the Condition for Bijection
For a bijection to exist from set A to set B, the number of elements in set A must be equal to or greater than the number of elements in set B. This is because each element in set A must map to a unique element in set B, and there must be enough elements in A to cover all elements in B.

### Step 4: Compare the Sizes of the Sets
In this case:
- Number of elements in A = 5
- Number of elements in B = 6

Since 5 (the number of elements in A) is less than 6 (the number of elements in B), it is impossible to create a one-one and onto mapping from A to B.

### Step 5: Conclusion
Since a bijection cannot exist under these conditions, the number of one-one and onto mappings from A to B is 0.

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

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