EricKryk wrote:![Image](https://snag.gy/4Cpv4.jpg)
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
First recognize that, in order to get from point X to point Y, we MUST travel through points A,B,C,D,E and F.
So, we can take the task of getting from point X to Y and break it into stages.
Stage 1: Move from point X to point A
There's only 1 possible route, so we can complete stage 1 in
1 way.
Stage 2: Move from point A to point B
There are 2 possible routes, so we can complete stage 2 in
2 ways.
Stage 3: Move from point B to point C
There's only 1 possible route, so we can complete stage 3 in
1 way.
Stage 4: Move from point C to point D
There are 2 possible routes, so we can complete stage 4 in
2 ways.
Stage 5: Move from point D to point E
There's only 1 possible route, so we can complete stage 5 in
1 way.
Stage 6: Move from point E to point F
There are 3 possible routes, so we can complete stage 6 in
3 ways.
Stage 7: Move from point F to point Y
There's only 1 possible route, so we can complete stage 7 in
1 way.
By the Fundamental Counting Principle (FCP), we can complete all 7 stages (and thus move from point X to point Y) in
(1)(2)(1)(2)(1)(3)(1) ways ([spoiler]= 12 ways[/spoiler])
Answer:
C
Cheers,
Brent
Aside: For more information about the FCP, watch our free video:
https://www.gmatprepnow.com/module/gmat-counting?id=775