Question

You are planning a day of shopping. You will visit the following six ​stores: Meijer comma JCPenney comma Lowes comma Follett's comma Costco comma and Kohl's. Since Costco and Lowes are right next to each​ other, you will definitely visit these two stores consecutively. How many different itineraries can you plan for your​ day?

Answer 1

Answer: 240

Explanation:

Planning an itinerary is the same as choosing an order in which you will visit the shops. To count all the possible orders, we use the multiplication principle.

There are 6 different shops, but we can think of Costco and Lowes as being the same place on the itinerary because they are always visited together. However, given that the order matters, there are 2 possibilities: visiting Costco first and then Lowes, or visiting Lowes first and Costco second.

Now, there are 5 choices for the first place. The second place can't be the same as the first one, so there are 4 choices for it. The third place must be different from the previous two, so there are 3 choices for it. Similarly, there are 2 choices for the fourth place and 1 choice for the last place, so using the multiplication principle there are $5\cdot 4\cdot 3 \cdot 2\cdot 1$ ways to visit these places.

Finally, to create an itinerary, we must take into account the order between Costco and Lowes and the order of the 5 places, so by the multiplication principle there are $2\cdot 5\cdot 4\cdot 3 \cdot 2\cdot 1=240$  itineraries.

Keywords: multiplication principle