27. In how many ways can 6 people be seated on six chairs?
27. The first person can choose a chair in six ways, the second in five ways, and so on. Finally, only one chair will remain for the sixth person. In total, we get $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1=720$ ways.

Note. The product of the first $n$ natural numbers is denoted by $n$! (read: n factorial). Thus, $6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1=6!$.