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Home » Let \( w \) represent the width of the garden. Then, the length is \( 3w \). - AMAZONAWS

Let \( w \) represent the width of the garden. Then, the length is \( 3w \). - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 \frac{5!}{2! \cdot 2! \cdot 1!} = \frac{120}{4} = 30

📌 However, we are given a constraint: **both roses must be visited before any lily**. This means the first appearance of a lily must come after the last rose.

📌 We proceed by counting the number of valid relative orders of roses (R₁, R₂) and lilies (L₁, L₂), treating them as distinguishable only by type, with the condition that all R's precede all L's.

📌 Step 1: Fix the relative order of R's and L's.

📌 The condition is that both R's come before both L's — that is, in the sequence, every R appears before every L. This is more restrictive than just "the two R’s together" or "R’s clustered."

📌 The positions of the 4 R and L flowers (2 R, 2 L) must be such that all R’s occupy the earliest 2 of these 4 positions, and the L’s occupy the last 2.

📌 But since the types are indistinguishable, we count the number of ways to assign positions to the types under the constraint.

📌 Alternative approach:

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