How many orders are possible for trying (5) distinct keys in (5) distinct locks if each key is tried exactly once?

Correct answer: 120

This asks for the number of orders in which 5 distinct keys can be tried. There are 5 choices for the first position, then 4, 3, 2, and 1 choices. Thus, the total number of orders is \(5\times4\times3\times2\times1=5!=120\). Option 60, or \(5!/2\), would arise only if an extra condition made two orders equivalent; no such condition is given here. Exam tip: use \(n!\) when all \(n\) distinct objects are arranged once in order.