<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, and passes through Ocean Heights in both directions, and does not travel any road twice, how many different routes for the trip are possible?</p>
<p>A. 72 (right answer)
B. 36
C. 24
D. 18
E. 12</p>
<p>I understand this question has been brought up and resolved but i dont quite get why we must subtract 1 from 3 and 4 on the way back. Why not 2? Since we already multiplied 3 by 4, shouldnt ALL the roads be covered? how is it possible that martina travel back in anyway without traveling the same road twice?!</p>
<p>When we multiplied 3 by 4, that was to find how many possible ways Martina could get from Plattsville to Ocean Heights. She has to pick one of them. So, not all the roads are covered.</p>
<p>Here’s the explanation for how to do the problem. Read it over, and I think you’ll understand where I’m coming from.</p>
<p>Okay, first she has to get from Plattsville to Ocean Heights to Bay Cove, right? Well, for every 3 ways she can go to Plattsville to Ocean Heights, she can go 4 ways from O to B, so there are 12 ways total for her to go from P to O to B.</p>
<p>Now, on the return trip, she needs to go from Bay Cove to Ocean Heights. Well, she’s already taken one of the roads from Ocean Heights to Bay Cove, so now instead of 4 options, she can only choose among the 3 roads that go from Bay Cove to Ocean Heights. 12x3 = 36. Okay, so she picked one road and is now at Ocean Heights and has to go back to Plattsville. </p>
<p>Now, she took one of the 3 roads from Plattsville to Ocean Heights already, leaving her with only 2 roads left. 36x2= 72, which is the correct answer.</p>
<p>Oh i see, so the 12 just tells us how many ways she can do this cat and mouse game, and since she took 1 at plat and 1 after ocean, theres only 3 and 2 roads back! </p>