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Math Help - How many combinations contain specific numbers?

  1. #1
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    How many combinations contain specific numbers?

    Given are all possible combinations of 5 numbers from 1-35, all contained in combinations of 6 numbers (from 1-35). How many of the six number combinations contain 5 specific numbers?
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  2. #2
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    Quote Originally Posted by askjohn View Post
    Given are all possible combinations of 5 numbers from 1-35, all contained in combinations of 6 numbers (from 1-35). How many of the six number combinations contain 5 specific numbers?
    Is it possible to give a clearer statement of this question?
    As it reads now, you are asking “how many combinations of six contain a particular combination of given numbers?” The answer to that is 30.
    But I cannot imagine that is what the question means. Is it?
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  3. #3
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    Well, I'm a bit confused! That's what I thought at first too.

    Since we are dealing with six number combinations, each one of which contains 6 possible combinations of five numbers, the total number of combinations of six containing all the combinations of five would be 324632 (35c5) / 6 = 54105 combinations of six; However, 35c6 would be 1623160.

    So, if 30 were the answer to the first option, what would happen if we had all the combinations of 6 instead? Would it just be the same?
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  4. #4
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    I just do not know what the OP means.
    Is that an exact wording or is it a translation?
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  5. #5
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    It's a translation.

    Let me paraphrase.

    We have all the possible combinations of five numbers from 1 to 35 (35c5) contained in combinations of six numbers.
    for example: 1 2 3 4 5 6 (contains {1,2,3,4,5} {1,2,3,4,6} {1,2,3,5,6} {1,2,4,5,6} {1,3,4,5,6} {2,3,4,5,6})

    What I want to know is how many of these -six- number combinations contain -five- specific numbers. Logically its 30. I'm confused however with the fact that every >1< combination of 6 contains 6 combinations of five!!
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  6. #6
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    There are six combinations of six objects taken five at a time.
    \dbinom{6}{5}=\dfrac{6!}{5!\cdot 1!}=6
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  7. #7
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    Hello, askjohn!

    The wording is confusing.
    All that emphasis on subsets of 5 numbers . . .


    Given are all possible 6-number subsets of numbers from 1-35,
    how many of these subsets contain 5 specific numbers?

    What do you mean by "logically it's 30"? .Is that the correct answer?


    Here's my reasoning . . .

    The is one way to get the five specific numbers.
    The sixth number can be any of the remaining 30 numbers.

    Therefore, the answer is 30.
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  8. #8
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    You're right! It's so simple.. I just got confused by the subsets within the subsets! thanks!
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