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How many different Lunches from the Lunch Menu

  1. Aug 13, 2017 #1
    1. The problem statement, all variables and given/known data
    A diner serves a lunch special, consisting of soup or salad, a sandwich, coffee or tea and a dessert. If the menu lists 3 soups , 2 salads, 7 sandwiches and 8 desserts, how many different lunches can you choose?

    2. Relevant equations
    Counting Principle

    3. The attempt at a solution
    Sandwiches = 7
    Deserts = 8
    The above two are without 'or' so their combinations = 56.
    Combining 2 Salads = 56 * 2 = 112
    or Combining 3 soups = 56 * 3 = 168
    Total = 112 + 168 = 280

    but answer is wrong. Some body please guide me.

    Zulfi.
     
  2. jcsd
  3. Aug 13, 2017 #2

    phinds

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    what is 5x7x2x8 ?
     
  4. Aug 13, 2017 #3
    Hi,
    I know about 7, 2 & 8 but i dont know whats 5?

    Zulfi.
     
  5. Aug 13, 2017 #4

    SammyS

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    You are missing one choice.
     
  6. Aug 13, 2017 #5
    Hi,
    Are you talking about tea and coffee? No quantity mentioned about them so i have not included them.

    Zulfi.
     
  7. Aug 13, 2017 #6

    SammyS

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    Yes. That's what I'm referring to.
     
  8. Aug 13, 2017 #7

    Ray Vickson

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    It said that each meal includes either tea or coffee, so you cannot neglect them.
     
  9. Aug 13, 2017 #8

    phinds

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    5 = 3 + 2
     
  10. Aug 13, 2017 #9

    haruspex

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    In case it is not clear from the previous replies, you have two errors. Ray and Sammy are pointing out that you have omitted the tea/coffee choice, while phinds is drawing attention to the fact that soup and salad are mutually exclusive.
     
  11. Aug 15, 2017 #10
    Hi,
    Thanks all for your help. Tea/Coffee: what is their quantity? If i say that each is one, then there is no effect. I dont know what you mean by mutual Exclusive. In computer this is used for shareable device used one at a time.
    Please guide me.

    Zulfi.
     
  12. Aug 15, 2017 #11

    haruspex

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    It means you cannot have both. It says "soup or salad". If there are 3 soups and two salads, how many different things can you choose?
    You can have tea or coffee. How many different things can you choose?
     
  13. Aug 15, 2017 #12
    Hi,
    <It means you cannot have both. It says "soup or salad". If there are 3 soups and two salads, how many different things can you choose?>
    If there are 3 soups S1, S2 & S3 & 2 Salads C1, C2 then it means i cant have:
    S1C1, S1C2, S2C1, S2C2, S3C1, S3C2
    So i have to take each of them alone so there are 5 five choices now:
    S1, S2, S3, C1, C2 and tea or coffee, i have 2 choices:
    Tea1, Coffee1
    7 * 8 * 5 * 2 = 560
    Thanks.
    Zulfi.
     
  14. Aug 15, 2017 #13

    haruspex

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    Good.
     
  15. Aug 15, 2017 #14

    phinds

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    Exactly. See post #2 in which my point was that you were making this problem harder than it is.
     
  16. Aug 15, 2017 #15
    Yes my friend, thanks for your response. Actually i already have the solution, but i cant understand it so i was looking for more details.

    Zulfi.
     
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