SOLUTION: There are 7 different restaurants in the X City. Part a. You want to choose 2 different restaurants from them. In how many different ways can you do that? Part b. You want to c

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Question 1198227: There are 7 different restaurants in the X City.
Part a. You want to choose 2 different restaurants from them. In how many different ways can you do that?
Part b. You want to choose two different restaurants to eat your lunch in the first one of them and your dinner in the second one of them. In how many different ways can you do that?
Part c. You want to choose two restaurants to eat your lunch in the first one of them and your dinner in the second one of them. The restaurants do not have to be different - you are OK to eat lunch and dinner in the same restaurant. In how many different ways can you do that?
Answer by ikleyn(52802) About Me  (Show Source):
You can put this solution on YOUR website!
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There are 7 different restaurants in the X City.

Part a. You want to choose 2 different restaurants from them. 
        In how many different ways can you do that?

Part b. You want to choose two different restaurants to eat your lunch in the first one of them 
        and your dinner in the second one of them. In how many different ways can you do that?

Part c. You want to choose two restaurants to eat your lunch in the first one of them 
        and your dinner in the second one of them. The restaurants do not have to be different 
        - you are OK to eat lunch and dinner in the same restaurant. In how many different ways can you do that?
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(a)  In this scenario, they ask you 

        +-----------------------------------------------------------+
        |  how many different pairs can you make from n=7 items     |
        |  if the order doesn't matter and repeating is prohibit ?  |
        +-----------------------------------------------------------+


     This number is  %28n%2A%28n-1%29%29%2F2 = %287%2A%287-1%29%29%2F2 = %287%2A6%29%2F2 = 7*3 = 21.    ANSWER

     It is the same as the number of combinations from 7 items taken 2 at a time.



(b)  In this scenario, they ask you 


        +-----------------------------------------------------------+
        |  how many different pairs can you make from n=7 items     |
        |  if the order does matter and repeating is prohibit ?     |
        +-----------------------------------------------------------+


     This number is  n%2A%28n-1%29 = 7%2A%287-1%29 = 7*6 = 42.                            ANSWER

     You can choose 1st restaurant in 7 ways and the second restaurant in 6 ways.



(c)  In this scenario, they ask you 


        +-----------------------------------------------------------+
        |  how many different pairs can you make from n=7 items     |
        |  if the order does matter and repeating is allowed ?      |
        +-----------------------------------------------------------+


     This number is  n*n = n%5E2 = 7*7 = 7%5E2 = 7*6 = 49.                        ANSWER

     You can choose 1st restaurant in 7 ways and the 2nd restaurant in 7 ways.

Solved, with complete explanations.