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2021 AMC Fall 10B Problem 23

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2021 AMC Fall 10B Problem 23AMC 10 Step by Step
Name:                             Date: September 13, 2026
Basic Probability · difficulty 4 of 5 · about 7 min · position P21-25

Each of the 55{ } sides and the 55{ } diagonals of a regular pentagon are randomly and independently colored red or blue with equal probability. What is the probability that there will be a triangle whose vertices are among the vertices of the pentagon such that all of its sides have the same color?

  1. A)

    23\frac23

  2. B)

    105128\frac{105}{128}

  3. C)

    125128\frac{125}{128}

  4. D)

    253256\frac{253}{256}

  5. E)

    11

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