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MathNet 2007-part-01 — 187 problems (EN–VI) Question 19

Math Olympiad Vault · MathNet 2007-part-01 — 187 problems (EN–VI)

Question 19

Eight children, all of different heights, must form a line ordered from shortest to tallest. We say that the line has exactly one error if there is one child who stands immediately behind a taller one, and all the others (except the first in line) stand immediately behind a shorter one. In how many ways can the eight children form a line with exactly one error?