Question 109

ABCDE is a pentagon. There are 5 paths connecting A and B, 4 paths connecting B and C, 6 paths connecting C and D, 5 paths linking D and E, 3 paths connecting E and A. Also, 3 paths joining A and C. If an ant starting from A is always heading towards point C, how many different valid routes can it take?

Name: ABCDE is a pentagon. There are 5 paths connecting A and B, 4 paths connecting B and C, 6 paths connecting C and D, 5 paths linking D and E, 3 paths connecting E and A. Also, 3 paths joining A and C. If an ant starting from A is always heading towards point C, how many different valid routes can it take?
Uploaded: 2026-06-14T12:14:34.538767+05:30
Duration: 5 min 31 s
Description: ABCDE is a pentagon. There are 5 paths connecting A and B, 4 paths connecting B and C, 6 paths connecting C and D, 5 paths linking D and E, 3 paths connecting E and A. Also, 3 paths joining A and C. If an ant starting from A is always heading towards point C, how many different valid routes can it take?

Solution

In this scenario, the ant has three options:

1) Go to C directly from A, for which it has 3 paths.

2) Use the path A-B-C, for which it has 5$$\times\ $$4, which is 20 paths.

3) Use the path A-E-D-C, for which it has 3$$\times\ $$5$$\times\ $$6, or 90 paths.

Adding the above numbers, we get 113 as the total number of ways in which the ant can reach C from A.

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