A residents' welfare association of 12 members must appoint a president, a secretary and a treasurer, no member being given more than one post. In how many ways can the three posts be filled?

The three posts are different, so who gets which post matters: the president can be any of 12, the secretary any of the remaining 11 and the treasurer any of the remaining 10, giving $12\times 11\times 10=1320$. Trap $220=C(12,3)$ merely picks the three office-bearers as an unordered set and loses the distinction between the posts. Trap $1728=12^3$ lets one member hold two posts. Trap $132=12\times 11$ fills only two of the three posts.