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Home » Area of the square not covered by the circle: - Blask

Area of the square not covered by the circle: - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \text{Total panels} = 10 \times 15 = 150

📌 So, 150 distinct panels can be formed.

📌 An urban forestry researcher photographs trees in a grid of 4 rows and 3 columns. If she selects 3 non-overlapping 1×1 grids (positions) at random, what is the probability that all 3 are in different rows?

📌 Total number of 1×1 grid positions: \( 4 \times 3 = 12 \).

📌 Number of ways to choose 3 distinct positions: \( \binom{12}{3} = \frac{12 \times 11 \times 10}{6} = 220 \).

📌 Now, favorable outcomes: all 3 positions in different rows.

📌 There are 4 rows, choose 3 distinct rows: \( \binom{4}{3} = 4 \).

📌 Each chosen row has 3 columns, so for each row, pick 1 position: \( 3 \times 3 \times 3 = 27 \).

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This is a classic recurrence problem.
Let $ a_n $ be the number of valid sequences of length $ n $ with 4 ch...
For the first layer: 4 choices.
For each subsequent layer: 3 choices (different from the previous).
So total: $ a_5 = 4 \cdot 3^4 $
Compute: $ 3^4 = 81 $, $ 4 \cdot 81 = 324 $
Thus, the number of valid fossil selections is $ \boxed{324} $.
\boxed{324}
Question: How many 6-digit positive integers have all digits either 3...
Solution: First, total number of 6-digit numbers with digits only 3 or...

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