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MathNet 2025-part-01 — 187 problems (EN–VI) Question 50

Math Olympiad Vault · MathNet 2025-part-01 — 187 problems (EN–VI)

Question 50

In how many ways can one choose 5 numbers from the list
$\frac{1}{8}, \frac{1}{7}, \frac{1}{6}, \frac{1}{5}, \frac{1}{4}, \frac{1}{3}, \frac{1}{2}, 1, 2, 3, 4, 5, 6, 7, 8$
so that the product of the chosen numbers is 1?

*Remark:* Two choices are considered different if one choice contains a number that the other choice does not. The order of numbers is not important.