The number of possible distinct shots may be calculated from the total number of diamonds (18) plus an extra "diamond" for each pocket (6). So there are 24x23 = 552 possible shots. But, remembering that shots to diamonds on the same rail are forbidden...(?!), that shots into pockets and straight into rails are trivial, and that the table exhibits four fold rotation symmetry,
-- part contents for card part 9
----- text -----
the total number of distinct shots is
at most 73. Actually, knowing only 23 of them will help you figure out the rest with a great degree of accuracy. Knowing only 15 will allow you to kick at balls with more efficiency than most nine ball players I play with.