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Thread: Homework Problem: In how many different patterns can these flowers be planted?

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    Homework Problem: In how many different patterns can these flowers be planted?

    Hello, I am unsure what category this would fall into, but it is a word problem and I can't seem to understand it at all. Please help, and thank you!

    Karmen and her mother are planting flowers in their backyard. They have 2 rose bushes, 3 tulip plants and 2 sunflowers. In how many different patterns can these flowers be planted?

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    Quote Originally Posted by Hailey1411 View Post
    Hello, I am unsure what category this would fall into, but it is a word problem and I can't seem to understand it at all. Please help, and thank you!

    Karmen and her mother are planting flowers in their backyard. They have 2 rose bushes, 3 tulip plants and 2 sunflowers. In how many different patterns can these flowers be planted?
    Are the flowers to be planted in one row?

    For example, since there are 7 plants you can plant 6 in a circle and one at the center, or 4 in row and 3 in next row, or .....
    Last edited by Subhotosh Khan; 01-13-2018 at 10:09 AM.
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
    Quote Originally Posted by Subhotosh Khan View Post
    Are the flowers to be planted in one row?

    For example, since there are 7 plants you can plant 6 in a circle and one at the center, or 4 in row and 3 in next row, or .....

    Yes, the flowers are to be planted in one row.

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    Quote Originally Posted by Hailey1411 View Post
    They have 2 rose bushes, 3 tulip plants and 2 sunflowers.
    Easier if you use numbers, like:
    1's = rose, 2's = sunflowers, 3's = tulips
    Make first arrangement: 1 1 2 2 3 3 3
    Next : 1 1 2 3 2 3 3
    I'm just an imagination of your figment !

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    Quote Originally Posted by Hailey1411 View Post
    Hello, I am unsure what category this would fall into, but it is a word problem and I can't seem to understand it at all. Please help, and thank you!

    Karmen and her mother are planting flowers in their backyard. They have 2 rose bushes, 3 tulip plants and 2 sunflowers. In how many different patterns can these flowers be planted [in one row]?
    You haven't given us any idea how much you have learned about this topic. Have you seen a formula or method for counting the number of ways letters, like RRSSTTT, can be arranged? Are you familiar with permutations and combinations? The more you tell us of what you know and where you are stuck, the more quickly we can help you use what you know to get started.

  6. #6
    Quote Originally Posted by Dr.Peterson View Post
    You haven't given us any idea how much you have learned about this topic. Have you seen a formula or method for counting the number of ways letters, like RRSSTTT, can be arranged? Are you familiar with permutations and combinations? The more you tell us of what you know and where you are stuck, the more quickly we can help you use what you know to get started.
    I haven't seen a formula or method, and I am not familiar with permutations or combinations. I don't know very much about this topic at all.

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    Quote Originally Posted by Hailey1411 View Post
    I haven't seen a formula or method, and I am not familiar with permutations or combinations. I don't know very much about this topic at all.
    Okay, since this is homework, you must have been taught something that would be useful. Can you tell us what you do know, that you think you might be expected to use here? What topic have you been learning?

    If there is nothing, then probably you are just expected to try listing possibilities. I would use the letters to represent the plants, as I suggested, and find an orderly way to list ways to arrange them:

    RRSSTTT
    RRSTSTT
    RRSTTST
    ...

    The number you're looking for will require a fairly long list (over 200), but it's not out of the question.

    If you do know anything at all about counting arrangements, though, that would probably be easier.

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    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by Hailey1411 View Post
    I haven't seen a formula or method, and I am not familiar with permutations or combinations.
    Was this exercise given to you in some math course? It's not really fair for students, when schools assign problems dealing with topics not covered in class!

    You need to study some lessons, before trying to understand how to count arrangements.

    Try googling keywords permutations with repetition, and look for written lessons or videos that you can understand. Work through the given examples, step by step, using paper and pencil. Make sure you understand the steps, before moving on. Once you have some idea about what you're supposed to be doing, try your exercise again. If you get stuck, you can then come back here and show us what you tried or explain why you're stuck. If you see something in a lesson or example that you don't understand, let us know.

    If the topic of counting permutations with repetition seems too confusing, then back up and start your search for lessons on basic counting principles and difference between combinations and permutations. If you cannot locate any lessons that help, please chat up your instructor.

    This forum is not an on-line classroom. We provide tutoring. In general, the volunteers here don't have time to type up lectures about general topics or to duplicate lessons that already exist in many forms and locations on the Internet.
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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    I agree with mmm. When this kind of vaguely worded problem is given without any prior training about counting principles, it is merely an excuse for a trained teacher to lord it over the students whom he or she has deliberately left in ignorance. Fortunately very, very few teachers are so lacking in self-esteem as to give problems that have not been previously explained in principle to students. If you have been cursed with a teacher whose self-regard demands giving problems to students without having previously given to them the concepts and tools needed to solve those problems, drop the course immediately.

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