counting problems

Test Preparation SAT Preparation
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<p>^^not sure if you can see that, it’s a counting problem…</p>

<p>The figure above shows all roads between Quarryton, Richfield, and Bayview. Martina is traveling from Quarryton to Bayview and back. How many different ways could she make the round trip, if she goes through Richfield exactly once and does not travel any section of road more than once?</p>

<p>the questions like these ALWAYS screw me up because I always get confused with the counting part. anyone have some tips?</p>

<ul>
<li>also i get trouble on the series problems.</li>
</ul>

2

<p>With counting questions, you have to ask yourself how many choices you have for each decision. And this time, you have to realize that you can go “clockwise” or “counter-clockwise”.</p>

<p>Say you go clockwise starting from Quarryton. You start out with 3 roads to choose from. Then once you are in Richfield you have 2 choices and then in Bayvile you have only 1 choice. So there are 3 x 3 x 1 = 6 ways to make the round trip clockwise. But you could also do each one in reverse (counterclockwise) so it’s 6 x 2 = 12 paths.</p>