 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability/1/e/ii/solution

m = n

, list the elements of

A

and choose their distinct images in

n, n - 1, \dots, 1

ways. Thus

# {bijections A \to B} = {n! 0 m = n, m \neq = n .

The factorial convention

0! = 1

includes the unique bijection from the empty set to itself.

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