If `n(A)=4" and "n(B)=6`. Then, the number of one-one function from A to B is

Options

A. 24
B. 60
C. 120
D. 360

Explanation

To find the number of one-one functions from set A to set B, we can use the formula for permutations since a one-one function requires that each element in set A maps to a unique element in set B.

### Step-by-step Solution:

1. **Identify the number of elements in sets A and B**:
- Given: \( n(A) = 4 \) and \( n(B) = 6 \).

2. **Check the condition for one-one functions**:
- For a one-one function to exist from set A to set B, the number of elements in set B must be greater than or equal to the number of elements in set A. Here, \( n(B) > n(A) \) (6 > 4), so one-one functions are possible.

3. **Use the formula for one-one functions**:
- The number of one-one functions from set A to set B can be calculated using the permutation formula:
\[ n(B) P n(A) = \frac{n(B)!}{(n(B) - n(A))!} \]
- In our case, this becomes:
\[ 6 P 4 = \frac{6!}{(6 - 4)!} = \frac{6!}{2!} \]

4. **Calculate the factorials**:
- Calculate \( 6! \) and \( 2! \):
\[ 6! = 720 \quad \text{and} \quad 2! = 2 \]

5. **Substitute the values into the formula**:
- Now substitute the factorial values into the permutation formula:
\[ 6 P 4 = \frac{720}{2} = 360 \]

6. **Conclusion**:
- Therefore, the number of one-one functions from set A to set B is \( 360 \).

### Final Answer:
The number of one-one functions from A to B is \( 360 \).

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