The Daytona 500, the season opening NASCAR event, has 43 drivers in the race. In how many different ways could the top four finishers (first, second, third, and fourth place) occur?

Approach Follow the flowchart in Figure 17.

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Figure 17 Are you making a sequence of choices? Yes Are the number of choices at each stage independent of previous choices? No Does the order of arrangements matter? Yes Use the Multiplication Rule of Counting (p.q.r....) Use tree diagram No n! Only r nPr (n-r)! Are you selecting all n objects, or only r objects? n! Yes Yes All n Are the objects all distinct? No No n! nCr= r!(n-r)! n! n! n!...nk!