If A and B are finite sets such that n(A)=5 and n(B)=7,then find the number of functions from A to B.

Answer

To find the number of functions from set A to set B, we can use the following reasoning:

1. **Understanding the Sets**: We have two finite sets, A and B. The number of elements in set A is given as \( n(A) = 5 \) and the number of elements in set B is given as \( n(B) = 7 \).

2. **Defining a Function**: A function from set A to set B assigns each element of A to exactly one element of B. This means that for every element in A, we can choose any element from B.

3. **Choosing Elements**: Since there are 5 elements in A, and for each of these elements, we can choose any of the 7 elements from B, we can calculate the total number of functions.

4. **Calculating the Total Functions**: The total number of functions from A to B can be calculated using the formula:
\[ \text{Total Functions} = (n(B))^{n(A)} \]
Substituting the values we have:
\[ \text{Total Functions} = 7^5 \]

5. **Calculating \( 7^5 \)**: Now we need to compute \( 7^5 \):
\[ 7^5 = 7 \times 7 \times 7 \times 7 \times 7 = 16807 \]

6. **Final Answer**: Therefore, the number of functions from set A to set B is \( 16807 \).

### Summary of Steps:
1. Identify the number of elements in sets A and B.
2. Understand that each element in A can map to any element in B.
3. Use the formula for the number of functions from A to B.
4. Compute the power \( 7^5 \).
5. State the final result.