ISL 1989 Problem 44

Given two distinct numbers $b_1$ and $b_2$ , their product can be formed in two ways: $b_1 \times b_2$ and $b_2 \times b_1.$ Given three distinct numbers, $b_1, b_2, b_3,$ their product can be formed in twelve ways:

$b_1\times(b_2 \times b_3);$ $(b_1 \times b_2) \times b_3;$ $b_1 \times (b_3 \times b_2);$ $(b_1 \times b_3) \times b_2;$ $b_2 \times (b_1 \times b_3);$ $(b_2 \times b_1) \times b_3;$ $b_2 \times(b_3 \times b_1);$ $(b_2 \times b_3)\times b_1;$ $b_3 \times(b_1 \times b_2);$ $(b_3 \times b_1)\times b_2;$ $b_3 \times(b_2 \times b_1);$ $(b_3 \times b_2) \times b_1.$

In how many ways can the product of $n$ distinct letters be formed?