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askquestion Group Title

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).

  • one year ago
  • one year ago

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  1. wio Group Title
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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.

    • one year ago
  2. wio Group Title
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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

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

    • one year ago
  4. wio Group Title
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    Hmmm. See any flaws?

    • one year ago
  5. askquestion Group Title
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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 ?

    • one year ago
  6. askquestion Group Title
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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 ?

    • one year ago
  7. wio Group Title
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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.

    • one year ago
  8. wio Group Title
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    Can I ask you some questions? You can answer me the best you can.

    • one year ago
  9. wio Group Title
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    Suppose I gave you a choice between chocolate ice cream and blueberry ice cream... How many choices do you have?

    • one year ago
  10. wio Group Title
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    I mean options, how many options do you have?

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

    • one year ago
  12. wio Group Title
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    Nope, just answer my questions ok? It'll help you get to the solution.

    • one year ago
  13. wio Group Title
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    If I ask you if you want chocolate or blueberry, how many option do you have?

    • one year ago
  14. wio Group Title
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    It's not a trick question or anything, you have only 2 options in this case.

    • one year ago
  15. askquestion Group Title
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    13 ?

    • one year ago
  16. askquestion Group Title
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    if must a dozen, right?

    • one year ago
  17. wio Group Title
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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?

    • one year ago
  18. wio Group Title
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    (We are starting out small and working our way up)

    • one year ago
  19. askquestion Group Title
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    oooh , if how many flavors?

    • one year ago
  20. wio Group Title
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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?

    • one year ago
  21. askquestion Group Title
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    3 ?

    • one year ago
  22. wio Group Title
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    yeah, cause order doesn't matter right?

    • one year ago
  23. askquestion Group Title
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    ohyeaaah, i got that

    • one year ago
  24. wio Group Title
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    What about if there are n cones.... how many options?

    • one year ago
  25. wio Group Title
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    if there are 3 cones... how many options?

    • one year ago
  26. askquestion Group Title
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    n+1 ?

    • one year ago
  27. askquestion Group Title
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    but i think, in my case, the flavor has given,

    • one year ago
  28. wio Group Title
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    Sure.

    • one year ago
  29. askquestion Group Title
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    so, we must think about the order

    • one year ago
  30. wio Group Title
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    If you have 6 cones, how many possibilities with 2 flavors?

    • one year ago
  31. wio Group Title
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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.

    • one year ago
  32. askquestion Group Title
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    i thinks its different, if 2 blueberry and 1 chocolates, with 2 chocolates and 1 blueberry

    • one year ago
  33. askquestion Group Title
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    oke, can give me a time, some bussiness

    • one year ago
  34. bintang Group Title
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    7+8+9+10+11+12+13=70

    • one year ago
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