Let A be a finite set having $x$ elements and let B be a finite set having $y$ elements. What is the number of distinct functions mapping B into A.
- A. $x^y$
- B. $2^{(x+y)}$
- C. $y^x$
- D. $\frac{y!}{(y-x)!}$
Answer: A. $x^y$
Explanation: For each of the $y$ elements in B, there are $x$ choices in A. Total functions = $x \times x \times ... \times x$ ($y$ times) = $x^y$.