Network Paths Count

CAT 1991 Slot 1 · QA · Medium · Combinatorics

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What is the total number of ways to reach A to B in the given network?

  • Stage 1: Point A connects to 4 nodes in column 1.
  • Stage 2: Column 1 (4 nodes) connects straight to Column 2 (2 nodes each group, total 2 paths per node).
  • Stage 3: Column 2 connects to Column 3 (2 nodes) with 2 paths.
  • Stage 4: Column 3 connects to point B with 1 path.
  1. A.

    12

  2. B.

    16

  3. C.

    20

  4. D.

    22

Answer

B

Explanation

Using path multiplication across stages: Total paths=4×2×2×1=16\text{Total paths} = 4 \times 2 \times 2 \times 1 = 16

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