CAT 2001 | Question: 47

Question

The figure below shows the network connecting cities A, B, C, D, E and F. The arrows indicate permissible direction of travel. What is the number of distinct paths from A to F?

  

• A. $9$
• B. $10$
• C. $11$
• D. None of these

Answer 1

(E) = 1
(C) = (E) + 1 = 2
(D) = (C) + (E) = 3
(B) = 1 + (C) + (D) + (E) = 7
(A) = (B) + (D) = 10.

Comments

yes. good one :)

Answer 2

Answer 10

Comments

how?

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just counted number of directed path, nothing special :)

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okay :) but can be solved using dynamic programming :)

Answer 3

The number of distinct paths from $A\rightarrow F$ is :

1. $ABF$
2. $ABCF$
3. $ABCEF$
4. $ABEF$
5. $ABDEF$
6. $ABDCF$
7. $ABDCEF$
8. $ADCF$
9. $ADCEF$
10. $ADEF$

Option (B) is correct.