SAT Math Question

Test Preparation
1

<p>There are 3 roads from Plattsville to Ocean Heights and 4 roads from Ocean Heights to Bay Cove. If Martina drives from Plattsville to Bay Cove and back, passes through Ocean Heights in both directions, and does not travel an road twice, how many different routes for the trip are possible?</p>

<p>A) 72
B) 36
C) 24
D) 18
E) 12</p>

<p>The answer is A, but I don’t know how they get that answer. Please explain, preferrably a fast technique that wouldn’t require drawing all posibilities as that would cut down my time on working other problems.</p>

2

<p>bump…</p>

3

<p>im not sure but this seems to work
don’t trust me though ahha</p>

<p>use permutations</p>

<p>3!/2! X 4!/3! because there are 3 choices for the first and you can only choose one so n is how many and subtract r how many u can choose
then thee # available decreases so itsd 2!/1! X 3!/2!
so i think its
3! X 4! X 2! X 3!</p>

<hr>

<p>2!<em>__3!</em><em>1!</em>_2! BUT DON’T TRUST ME LOL</p>

4

<p>well i did 4! x 3 = 72… but maybe it’s a coincidence that it worked…</p>

5

<p>Well if there are 3 roads to Ocean Heights, and then 4 from there to Bay Cobe, that’s 3 * 4 or 12 ways so far to get there, but on the way back, you can only use 3 of the 4 roads from BC to OH, so you do 12 * 3 or 36 ways, and then back to the start you can only use 2 of the initial 3 roads, so 72</p>