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Home » 😂 These Funny Good Morning Memes Will Put a Smile on Your Face Before 9 AM! - Parker Core Knowledge

😂 These Funny Good Morning Memes Will Put a Smile on Your Face Before 9 AM! - Parker Core Knowledge

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Solution: The student is arranging a total of $5 + 4 + 3 = 12$ blocks, with indistinguishability within each color. The number of distinct towers is the multinomial coefficient:

📌 Question: An ichthyologist tags 7 fish in a reef: 2 clownfish, 3 parrotfish, and 2 angelfish. If she observes one tagged fish each day for a week, how many distinct sequences of observed species can occur, assuming fish of the same species are indistinguishable?

📌 Solution: The ichthyologist observes 7 fish over 7 days—2 clownfish (C), 3 parrotfish (P), and 2 angelfish (A). Since fish of the same species are indistinguishable, the number of distinct observation sequences is:

📌 Question: A circular park has 5 distinguishable trees planted around its perimeter and 3 indistinguishable benches to be placed among them. If rotations of the arrangement are considered identical, how many distinct arrangements are possible?

📌 Solution: First, fix one tree to account for rotational symmetry. Since the trees are distinguishable, fixing one eliminates rotational duplicates. The remaining 4 distinguishable trees can be arranged in $4! = 24$ ways around the circle.

📌 Now, we place 3 indistinguishable benches into the 5 gaps between the trees (since the trees form a circle, there are 5 gaps between adjacent trees). The number of ways to distribute 3 indistinguishable benches into 5 distinguishable gaps (with no restriction on how many per gap) is a stars and bars problem:

📌 Since the tree arrangements are fixed in relative order by rotation, and benches are placed in gaps (not among trees), and trees are already arranged with one fixed, the total number of distinct arrangements is:

📌 Solution: First compute each binomial coefficient:

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