There have been several questions regarding possible number of chess games. for example - Database of every possible move in chess

However Can there be an estimate on the number of "allowable" chess positions.

For example White Pawns cannot occupy first row and Black Pawns cannot occupy eighth row. If a given chess piece is occupying a square, then another chess piece cannot occupy that. Using simple elimination rules coded, can we have an estimate on the number of unique positions that chess pieces can have. Since they would be reducing in number. An upper bound on positions before applying any elimination rules would be sum of (64 C 32 + 64 C 32 ... + 64 C 2). This is less than 10^20. With elimination rules, they should be significantly lower.

Any ideas on how elimination rules be written for chess pieces?