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📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 3! = 3 \times 2 \times 1 = 6

📌 2! = 2 \times 1 = 2

📌 Substituting these into the combination formula:

📌 \binom{5}{3} = \frac{120}{6 \times 2} = \frac{120}{12} = 10

📌 Therefore, there are \(\boxed{10}\) different combinations of platforms that can be selected for the comparative study.

📌 Question:** A gardener in Massachusetts is planting 3 distinct types of flowers in a row: roses, daisies, and tulips. If each type must appear at least once, in how many ways can the gardener arrange the flowers in a single row?

📌 To solve this, we use the principle of counting arrangements with repetition, ensuring each type appears at least once. This involves permutations of the multiset.

📌 Assume \( r \) roses, \( d \) daisies, and \( t \) tulips, and we know \( r + d + t = 3 \) with \( r, d, t \geq 1 \).

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