Question

The diagram above shows the various paths along which a mouse can travel from point X, where it is released, to point Y, where it is rewarded with a food pellet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracing any point along a path?

• A. $6$
• B. $7$
• C. $12$
• D. $14$
• E. $17$

Answer 1

Answer: (C)

$12$

We can calculate the total number of ways by using the basic principle for counting by multiplication.

This we do by multiplying the total possible routes between every two nodes in the path form X to Y. (different node are named in the image )

X $\to$ A $\to$ C and X $\to$ B $\to$ C ------------- 2 ways

C to D has to be covered to move ahead.

D $\to$ E $\to$ G and D$\to$ F $\to$ G ------------- 2 ways

G to H has to be covered to move ahead.

H $\to$ I $\to$ J and H$\to$ J and H$\to$ K $\to$ J ------------- 3 ways

J to Y must be moved to reach Y.

So, total ways = $2\times 2\times 2\times 3=12$ (option C)