1988 AIME Problem 1

One commercially available ten-button lock may be opened by depressing -- in any order -- the correct five buttons. The sample shown below has \{1, 2, 3, 6, 9\} as its combination. Suppose that these locks are redesigned so that sets of as many as nine buttons or as few as one button could serve as combinations. How many additional combinations would this allow?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.