Solution: 2015 Winter Midterm - 3

Author: Michiel Smid

Question

Let $A$ be a set of 7 elements and let $B$ be a set of 15 elements. How many one-to-one (i.e., injective) functions $f : A \rightarrow B$ are there?

(a)

$9 \cdot 10 \cdot 11 \cdot 12 \cdot 13 \cdot 14 \cdot 15$

(b)

$10 \cdot 11 \cdot 12 \cdot 13 \cdot 14 \cdot 15$

(c)

$8 \cdot 9 \cdot 10 \cdot 11 \cdot 12 \cdot 13 \cdot 14 \cdot 15$

(d)

$9 \cdot 10 \cdot 11 \cdot 12 \cdot 13 \cdot 14$

There are 15 choices for the first element in A, 14 choices for the second element in A, and so on.

Thus, there are $15 \cdot 14 \cdot 13 \cdot 12 \cdot 11 \cdot 10 \cdot 9$ one-to-one functions.