Number of stable molecules of artificial molecule XY4
There are 5 ways to choose the central atom. 

Choosing the possible combinations of the other 4 items from 6 isotopes is complicated as this article explains. But it provides a formula for combinations with repetition that gives the answer of 126. 

This implies that there are 630 distinct isotope combinations in the molecule (assuming that we can distinguish combinations of isotopes with the same atomic number which is possible with high resolution mass spectroscopy). If only integer atomic numbers count then the distinguisahble combinations will be lower. But the easiest way to work that out is to do a Monte-Carlo simulation not to look up probability formulae.