1972 USAMO 第 3 题

A random number selector can only select one of the nine integers 1, 2, ..., 9, and it makes these selections with equal probability. Determine the probability that after $n$ selections ($n>1$), the product of the $n$ numbers selected will be divisible by 10.

随机数选择器只能选择九个整数 1, 2, ..., 9 之一，并且它以相等的概率做出这些选择。确定经过 $n$ 个选择 ($n>1$) 后，所选 $n$ 个数字的乘积能被 10 整除的概率。