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A figure consists of 7 identical regular hexagons arranged in a honeycomb pattern, with one central hexagon completely surrounded by 6 outer hexagons attached to its edges. If two distinct hexagons are chosen at random from this figure, the probability that they do not share a common edge is

Options

  1. A4 7
  2. B3 7
  3. C5 7
  4. D10 21

Correct answer

B. 3 7

Step-by-step solution

The total number of hexagons is 7 . The total number of ways to choose 2 distinct hexagons is ⁷C₂ = 21 . Now, we count the number of pairs of hexagons that share a common edge. The central hexagon shares an edge with each of the 6 outer hexagons, giving 6 adjacent pairs. The 6 outer hexagons form a closed ring around the center, so each outer hexagon shares an edge with its two neighbors in the ring. This gives another 6 adjacent pairs. Total number of adjacent pairs = 6 + 6 = 12 . The number of pairs that do not s

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