Extend Example 1.4-6 to an \(n\)-sided die. That is, suppose that a fair \(n\)-sided die is rolled \(n\) independent times. A match occurs if side \(i\) is observed on the \(i\) th trial, \(i=1,2, \ldots, n\).
(a) Show that the probability of at least one match is
(b) Find the limit of this probability as n increases without bound.
Step 1 of 3
For a normal die probability that there are no matches is ⅚
If it is rolled 6 times the probability that there are no matches is 6