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\(l = \frac403\). - Moon Smoking

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 A rectangles length is increased by 50% and its width is decreased by 20%. If the original dimensions were 8 meters by 5 meters, what is the new area?

📌 #### 48Question: An archaeologist discovers a set of $6$ distinct ancient Incan tools: $2 stone axes, $2 ceramic bowls, and $2 gold pectorals. If she wishes to display them in a row such that no two items of the same type are adjacent, how many valid arrangements are there?

📌 Solution: We are to arrange $6$ distinct items: $A_1, A_2$ (stone axes), $B_1, B_2$ (ceramic bowls), $C_1, C_2$ (gold pectorals), with the restriction that no two items of the same type are adjacent. Although the tools are distinct, they are grouped by type with two identical-looking items per type (but physically distinct due to being unique artifacts).

📌 This is a classic inclusion-exclusion or derangement-type problem with repeated types but distinct carriers.

📌 We are to count the number of permutations of the 6 distinct artifacts such that no two axes are adjacent, no two bowls are adjacent, and no two pectorals are adjacent.

📌 We use inclusion-exclusion over the three forbidden adjacencies.

📌 $T = 6! = 720$ be total permutations.

📌 Let $P_A$: event that $A_1$ and $A_2$ are adjacent,

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