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  • 3 years ago

An ice cream parlor sell ice creams with three different flavors: blue- berry, chocolates, and vanilla. How many ways are there to choose a dozen ice creams with at most six vanilla ice creams? (Note: one dozen consists of twelve ice creams).

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  1. wio
    • 3 years ago
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    I would suggest this method: How many ways are there with exactly 0 vanilla How many ways are there with exactly 1 vanilla How many ways are there with exactly 2 vanilla How many ways are there with exactly 3 vanilla ... How many ways are there with exactly 6 vanilla Then I would add them up.

  2. wio
    • 3 years ago
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    To find how many ways with n vanilla, we ask: How many ways to distribute 12-n ice creams amongst the 2 other flavors

  3. wio
    • 3 years ago
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    Perhaps something like this?\[ \Large \sum_{n=0}^{6} 2^{12-n} \]

  4. wio
    • 3 years ago
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    Hmmm. See any flaws?

  5. askquestion
    • 3 years ago
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    so 1) if a dozen consist the same flavor? chocolate and blueberry = 2 ways 2) if vanilla = 6, so x+ y = 12 , x for chocolates and y for bluberry? until if vanilla = 0 , so x+y = 12 ?

  6. askquestion
    • 3 years ago
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    2) if vanilla = 6, so x+ y = 6 , x for chocolates and y for bluberry? until if vanilla = 0 , so x+y = 12 ?

  7. wio
    • 3 years ago
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    You don't wanna think in terms of x+y=6. We aren't solving for the number of chocolates and blueberry. We are finding the total number of combinations.

  8. wio
    • 3 years ago
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    Can I ask you some questions? You can answer me the best you can.

  9. wio
    • 3 years ago
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    Suppose I gave you a choice between chocolate ice cream and blueberry ice cream... How many choices do you have?

  10. wio
    • 3 years ago
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    I mean options, how many options do you have?

  11. askquestion
    • 3 years ago
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    yeah, i think if x+y = 6 , with times and divide theory, (6+1)! / 6!1! ?

  12. wio
    • 3 years ago
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    Nope, just answer my questions ok? It'll help you get to the solution.

  13. wio
    • 3 years ago
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    If I ask you if you want chocolate or blueberry, how many option do you have?

  14. wio
    • 3 years ago
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    It's not a trick question or anything, you have only 2 options in this case.

  15. askquestion
    • 3 years ago
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    13 ?

  16. askquestion
    • 3 years ago
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    if must a dozen, right?

  17. wio
    • 3 years ago
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    If you are going to get 2 ice creams, and you get to chose a flavor for each, how many options do you have?

  18. wio
    • 3 years ago
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    (We are starting out small and working our way up)

  19. askquestion
    • 3 years ago
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    oooh , if how many flavors?

  20. wio
    • 3 years ago
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    There are 2 flavors, and 2 cones. You get to chose a flavor for each cone. How many possibilities are there?

  21. askquestion
    • 3 years ago
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    3 ?

  22. wio
    • 3 years ago
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    yeah, cause order doesn't matter right?

  23. askquestion
    • 3 years ago
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    ohyeaaah, i got that

  24. wio
    • 3 years ago
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    What about if there are n cones.... how many options?

  25. wio
    • 3 years ago
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    if there are 3 cones... how many options?

  26. askquestion
    • 3 years ago
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    n+1 ?

  27. askquestion
    • 3 years ago
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    but i think, in my case, the flavor has given,

  28. wio
    • 3 years ago
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    Sure.

  29. askquestion
    • 3 years ago
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    so, we must think about the order

  30. wio
    • 3 years ago
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    If you have 6 cones, how many possibilities with 2 flavors?

  31. wio
    • 3 years ago
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    But having a blueberry and a chocolate isn't any different than having a chocolate and a blueberry... this is what is meant by order doesn't matter.

  32. askquestion
    • 3 years ago
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    i thinks its different, if 2 blueberry and 1 chocolates, with 2 chocolates and 1 blueberry

  33. askquestion
    • 3 years ago
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    oke, can give me a time, some bussiness

  34. bintang
    • 3 years ago
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    7+8+9+10+11+12+13=70

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