Solution: 2015 Winter Midterm - 2

Author: Michiel Smid

Question

Let $A$ be a set of 7 elements and let $B$ be a set of 15 elements. How many functions $f : A \rightarrow B$ are there?

(a)

${15 \choose 7}$

(b)

$7^{15}$

(c)

$15^7$

(d)

$15!/7!$

For each element in A, there are output 15 choices in B.

Thus, there are $15^7$ functions.