Question

A delivery driver must travel from Source (S) to Destination (D).
Possible paths:
S → A → C → D,
S → B → C → D,
S → A → E → D,
S → B → F → D.
Rules:
1. A route cannot repeat a node.
2. A route cannot have more than 3 edges.
3. C cannot be visited if E is visited.
4. B cannot be used if F is used.
How many valid routes exist from S to D?

• A. 3
• B. 4
• C. 5
• D. 6

Hint:

When validating routes, check dependency constraints like “cannot use X if Y is used” independently for each path.

Answer 1

The Correct Option is A

Step 1: Split by the first move from S. Via A, both of A's two continuations (to C, to E) survive every rule, that branch contributes 2 valid routes.
Step 2: Via B, Rule 4 blocks the B-then-F continuation (since B and F cannot both appear), leaving only B-then-C, that branch contributes just 1 valid route.
Step 3: Add the two branches.
\[ 2 + 1 = \boxed{3} \]
Final Answer: 3.