Problem 14 of 25sta-014
Six runners enter a race with no ties. In how many different ways can first, second and third place be awarded?
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Solution walkthrough1:28
- There are three places to fill, one at a time. Order matters: first is not the same as third.
- Any of the runners can finish first, so the first slot has choices.
- The winner cannot also be second. That leaves runners, so choices.
- Two runners are placed, so remain for third: choices.
- Multiply the choices for each slot: .
- Traps: is , ignores the order, and is .