  We compute the number of rhombus tilings of a hexagon with sides
$a+2,b+2,c+2,a+2,b+2,c+2$ 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 $a+2$ rows and $b+2$
columns, with largest entry $\le c+2$, with a given number of entries $c+2$ in
the first row, a given number of entries 0 in the last column and a given
bottom-left entry.
