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MathNet 2018-part-01 — 181 problems (EN–VI) Question 160

Math Olympiad Vault · MathNet 2018-part-01 — 181 problems (EN–VI)

Question 160

In a shooting contest, 8 targets are arranged in two columns of 3 targets and one column of 2 targets. The rules are:
- The shooter freely chooses which column to shoot at.
- He must aim at the lowest target not yet hit.

Question illustration

a) If the shooter ignores the second rule, in how many ways can he choose just 3 positions among the 8 distinct discs to shoot at?

b) If the rules are followed, in how many ways can the 8 targets be hit?