Question

how many one-to-one correspondences are there between two sets with
a. 6 elements each?
b. c elements each? explain your reasoning.
a. there are □ one-to-one correspondences between two sets with 6 elements each.

Explanation:

Step1: Recall permutation formula

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

Step2: Substitute \(n = 6\)

For \(n = 6\), we calculate \(6!\) as follows:
\(6!=6\times5\times4\times3\times2\times1\)
First, \(6\times5 = 30\), then \(30\times4=120\), then \(120\times3 = 360\), then \(360\times2=720\), and finally \(720\times1 = 720\).

Answer:

720