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Home » Thus, the ratio of the volumes is \(\boxed{\frac1125}\). - AssociationVoting

Thus, the ratio of the volumes is \(\boxed{\frac1125}\). - AssociationVoting

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Therefore, the total number of different assignments is:

📌 A micropaleontologist analyzes sediment layers containing microfossils from 3 types: foraminifera (F), radiolarians (R), and diatoms (D). She examines a core sample divided into 9 distinct strata. If she selects exactly 3 strata to analyze using stable isotope ratios, such that all three fossil types appear in at least one selected stratum, how many such combinations of 3 strata exist, assuming each stratum contains exactly one fossil type and all types appear across the 9 strata?

📌 Thus, we must count the number of 3-element subsets of the 9 strata such that each subset contains exactly one F, one R, and one D.

📌 But the problem does not specify how many of the 9 strata contain each type. However, the condition all three fossil types appear in at least one selected stratum implies we are selecting 3 strata and want the probability or count of those subsets where the multiset of types includes all three. Since only one fossil appears per stratum, this means: the three selected strata must include one F, one R, and one D.

📌 Alternatively, a cleaner and standard combinatorics interpretation consistent with olympiad style:

📌 But unless we know how many strata have each type, we cannot compute this.

📌 However, the problem says: how many such combinations of 3 strata exist, assuming each stratum contains exactly one fossil type and all three types appear across the 9 strata — meaning the full set of 9 strata contains all types, but not necessarily uniformly.

📌 But again, without distribution, this is impossible.

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