Scott can travel from Rochester, N.Y., to New York City by bus, train, car, or airplane. He can travel from New York to London, England, by airplane or ship.
1. If Scott must return from London to New York by airplane, and from New York to Rochester by airplane, how many ways may he make the round trip?
Hmm. Looks like once he gets to London, there's only one way back. So, how many ways can he get to London?
4*2 = 8
Now, if we count the two legs by plane as a single "way", then he can get there
3*2 + 1 = 7
To determine the number of ways Scott can make the round trip, we need to consider the options he has for each leg of the journey.
1. The first leg is from Rochester to New York City. Scott has four options: bus, train, car, or airplane. Therefore, there are four possibilities for the first leg.
2. The second leg is from New York City to London. Scott has two options: airplane or ship. Therefore, there are two possibilities for the second leg.
3. The third leg is from London to New York. Since Scott must return by airplane, there is only one option for this leg.
4. The final leg is from New York to Rochester. Again, Scott must return by airplane, so there is only one option for this leg as well.
To find the total number of ways Scott can make the round trip, we multiply the number of possibilities for each leg:
4 (Rochester to New York) * 2 (New York to London) * 1 (London to New York) * 1 (New York to Rochester) = 8
Therefore, Scott can make the round trip in 8 different ways.