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# There are 3 roads from Pittsburgh to Ocean City, Md and

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Eternal Intern
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There are 3 roads from Pittsburgh to Ocean City, Md and [#permalink]  29 Jul 2003, 17:44
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There are 3 roads from Pittsburgh to Ocean City, Md and four roads from Ocean city, Md. to Bay City,CA. If Allison drives from Pittsburgh to Bay City, CA and back, passes from Ocean City in both directions, and does not travel any road twice, how many different routes for the trip are possible?

Hint: I thought 48, it is not
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Ride em cowboy

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[#permalink]  29 Jul 2003, 19:29

Let's subtract a 100 points from CEO's score and give it to me who needs the curve?
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Ride em cowboy

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[#permalink]  29 Jul 2003, 19:35
Expert's post
Curly05 wrote:
:wink:

Let's subtract a 100 points from CEO's score and give it to me who needs the curve?

Why do you need a curve if you are so smart?

So, is it 72?
Eternal Intern
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Son [#permalink]  29 Jul 2003, 20:22
Yes, CEO, tell us the story over a few beers!

72, is right, but you ran out of time
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Ride em cowboy

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[#permalink]  29 Jul 2003, 20:48
from P to B = 3*4=12
from B to P = (4-1)*(3-1)=6

12*6=72
Eternal Intern
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[#permalink]  30 Jul 2003, 05:22
Multiplication Principle!

Masked in disguise, am i right?
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Ride em cowboy

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[#permalink]  22 Jan 2004, 19:49
A different approach.

3 roads between A-B and 4 roads between B-C
A <---------> B <-------------> C

One road from between A-B can be chosen in 3C1 ways
One road between B-C can be chosen in 4C1 ways
Since these two roads cannot be taken during return journey
One road between C-B can be chosen in 3C1 ways
One road between B-A can be chosen in 2C1 ways
So we have total ways = 3C1 * 4C1 * 3C1 * 2C1 = 3*4*3*2 = 72
[#permalink] 22 Jan 2004, 19:49
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# There are 3 roads from Pittsburgh to Ocean City, Md and

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