Question

how many one - to - one correspondences are there between two sets with
a. 8 elements each?
b. n elements each? explain your reasoning.
a. there are □ one - to - one correspondences between two sets with 8 elements each.

Explanation:

Step1: Recall permutation formula

A one - to - one correspondence between two sets with \(n\) elements each is a permutation of \(n\) elements. The number of permutations of \(n\) elements is given by \(n!\) (read as \(n\) factorial), where \(n!=n\times(n - 1)\times(n - 2)\times\cdots\times1\).
For \(n = 8\), we need to calculate \(8!\).

Step2: Calculate \(8!\)

\(8! = 8\times7\times6\times5\times4\times3\times2\times1\)
First, \(8\times7 = 56\), then \(56\times6=336\), \(336\times5 = 1680\), \(1680\times4=6720\), \(6720\times3 = 20160\), \(20160\times2=40320\), \(40320\times1 = 40320\).

Answer:

40320