ITPEC IP October 2024 Question 4
ITPEC IP October 2024 — Question 4 of 100
There are 9 shortest paths from A1 to D4 via C2. The figure already shows that three shortest routes lead from A1 to C2. From C2 to D4, a shortest route must move two columns right and one row up, in any order. The three possible orders are right-right-up, right-up-right, and up-right-right.
Each of the three first segments can be combined with each of the three second segments. By the multiplication principle, the total is 3 × 3 = 9.
Answer (b)
Why not others:
- (a) 6 adds the two counts instead of combining independent path choices
- (c) 12 and (d) 20 count routes that are not shortest or overcount the allowed combinations
Key rule: For a route required to pass through a fixed node, multiply the number of shortest paths to that node by the number from that node to the destination.
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