A club of six members must elect a president, a vice president and a treasurer. In how many ways can the three posts be filled?

1. The three posts are distinct, so order matters and this is a permutation of 6 taken 3 at a time. 2. Six people could be president, five of the rest could be vice president, and four could be treasurer. 3. Multiplying gives 6 times 5 times 4 = 120. 4. The formula gives the same result: P(6, 3) = 6!/(6 - 3)! = 6!/3!. 5. Since 6! = 720 and 3! = 6, the quotient is 720/6 = 120. 6. Reporting 720 uses 6! alone, which lines up all six members rather than filling three posts. 7. Reporting 20 is C(6, 3), which ignores which of the three posts each person holds. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.5 Counting Principles_