A, B and C are three places such that there are three different roads from A to B, four different roads from…

A, B and C are three places such that there are three different roads from A to B, four different roads from B to C and three different roads from A to C. In how many different ways can one travel from A to C using these roads?
  1. 10
  2. 13
  3. 15
  4. 36

Solution

Direct routes from A to C = 3. Routes via B = (A to B) x (B to C) = $3 \times 4 = 12$. Total ways = 3 + 12 = 15.

Asked in: CSAT 2022

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