For questions 1 to 3 consider the town of Alpha. In Alpha one can eat at the fol

Question

For questions 1 to 3 consider the town of Alpha. In Alpha one can eat at the following places: Dave's Diner, Tony's Trottoria, Paulie's Pizzeria, Rick's Restaurant, Bob's Bistro, Pete's Pub, Gregg's Grill and Carl's Café. A visitor is spending the day in Alpha and will need to go out for breakfast, lunch and dinner 1) 2) How many different ways can the visitor choose restaurants to eat at-% point If the visitor doesn't want to eat at the same place more than once, how many different ways can he choose restaurants to eat at that satisfy this restriction?-½ point 3 Suppose the visitor is a food critic for a traveling publication and was sent to the town and charged with the task of reviewing 3 different restaurants for their service. Since he is only concerned with the service he does not care about which particular menu he is having (i.e. the breakfast menu, the lunch menu or the dinner menu). This being the case, how many different ways can he choose 3 different restaurants to review. _ ½ point

Explanation / Answer

1) Since, the visitor can have breakfast, lunch and dinner at any of the restaurants we can write:

At any restaurant he can have all three meals, so for every place he has 3 options (breakfast, lunch and dinner)

There are 8 restaurants, so

Number of ways = 3^8 = 6561

2) Now he can eat at a place only once, so each restaurant has only 1 option (either breakfast, lunch or dinner)

So, number of ways now = 8C3 * 3! = 336

3) Now it doesn't matter if he has breakfast, lunch and dinner at a particular place

Now we just have to choose 3 places out of 8

Ways = 8C3 = 56

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