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The diagram below shows the various paths along which a

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The diagram below shows the various paths along which a [#permalink] New post 25 Apr 2012, 07:54
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The diagram below 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 pallet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracting any point along a path?

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


I know my approach is wrong. Can you please help me understand why the permutation formula does not work for this problem? ( We are counting without replacement and the order matters, so I tried n!/(n-3)! where n=7

Thank you, all!
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Re: The diagram below shows the various paths along which a [#permalink] New post 25 Apr 2012, 08:15
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emil3m wrote:
The diagram below 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 pallet. How many different paths from X to Y can the mouse take if it goes directly from X to Y without retracting any point along a path?

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


I know my approach is wrong. Can you please help me understand why the permutation formula does not work for this problem? ( We are counting without replacement and the order matters, so I tried n!/(n-3)! where n=7

Thank you, all!


It's not clear what's you logic behind applying permutation to this problem. I guess 3 is # of the forks on the road, but we are not choosing those 3 out of 7 (?).

Anyway, the problem is about simple counting. There are 3 forks in the road: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

Answer: C.
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Re: The diagram below shows the various paths along which a [#permalink] New post 25 Apr 2012, 08:25
Bunuel wrote:
It's not clear what's you logic behind applying permutation to this problem. I guess 3 is # of the forks on the road, but we are not choosing those 3 out of 7 (?).

Anyway, the problem is about simple counting. There are 3 forks in the road: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

Answer: C.


7 paths to chose from and you must pick 3 to get to the destination..

I haven't seen a permutation problem yet in the OG, so maybe the difference in identifying when to use it will show when I see one.
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Re: The diagram below shows the various paths along which a [#permalink] New post 25 Apr 2012, 08:31
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emil3m wrote:
Bunuel wrote:
It's not clear what's you logic behind applying permutation to this problem. I guess 3 is # of the forks on the road, but we are not choosing those 3 out of 7 (?).

Anyway, the problem is about simple counting. There are 3 forks in the road: 2 choices for the first one, 2 for the second and 3 for the third. Hence total # of ways is 2*2*3=12.

Answer: C.


7 paths to chose from and you must pick 3 to get to the destination..

I haven't seen a permutation problem yet in the OG, so maybe the difference in identifying when to use it will show when I see one.


As you can see from the solution there are 12 different paths not 7. There are 2+2+3=7 different line segments separated by 3 forks.

As for permutation. Try Combinatorics chapter of Math Book for theory: math-combinatorics-87345.html

Also try some questions on combinations to practice:
DS: search.php?search_id=tag&tag_id=31
PS: search.php?search_id=tag&tag_id=52
Hard questions on combinations and probability with detailed solutions: hardest-area-questions-probability-and-combinations-101361.html (there are some about permutation too)

Hope it helps.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Re: The diagram below shows the various paths along which a   [#permalink] 25 Apr 2012, 08:31
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