Rhombus Tilings of a Hexagon with Three Fixed Border Tiles

We compute the number of rhombus tilings of a hexagon with sides a, b, c, a, b, c with three fixed tiles touching the border. The particular case a=b=c solves a problem posed by Propp. Our result can also be viewed as the enumeration of plane partitions having a rows and b columns, with largest entry ⩽c, with a given number of entries equal to c in the first row, a given number of entries equal to 0 in the last column, and a given bottom-left entry.