Variable Combinations in Regression

Let's say I have 8 variables and I want to generate all combinations  
of those variables (In pairs, threes fours, etc) to run in multiple  
linear regression. Is there a built-in function to do that in R?

The formula syntax allows that.

y ~ (x1 + x2 + x3 + x4 + x5)^2   for instance,  would give you all 5  
of the main effects and the ten two way interaction estimates. With  
the "exponent set to three you also get the three way interactions  
(although I have never tried this particular level of dredging.)  
Unless you have scientific arguments for higher level interactions,  
they are a major threat to interpretability and validity as well as a  
threat to convergence.

(With 8 variables you are going to experience a combinatorial  
explosion: 28 two-way terms, 56 3-way, 70 4-way and then down the  
other side of Pascal's triangle.)

Or at a minimum, how could I take those variables and generate all  
possible combinations.

Thank you for any assistance.

David Winsemius, MD
Heritage Laboratories
West Hartford, CT