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South African Mathematics Olympiad

South Africa statistics

Problem

If 8 athletes run a race and no two athletes finish exactly together, the number of different possible results for the first, second and third positions is (A) 360 (B) 300 (C) 56 (D) 336 (E) 512
Solution
There are 8 possibilities for first place, each of which can be combined with 7 possibilities for second place and 6 possibilities for third place. Thus the number of possible results for all three places is . (This assumes that no two athletes finish exactly together.)
Final answer
D

Techniques

Permutations