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Summer Clouds moderators

09/11/2017 at 08:42
Answers
2
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How many subsets containing an odd number of elements does a set with 10 elements have?




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  • ...
    Lê Quốc Trần Anh Coordinator 09/11/2017 at 17:57

    We can do this by using Pascal's triangle. The numbers from the tenth row of the triangle (corresponds to the number in the subsets) is:

    1    10   45   120   210   252   210   120   45   10   1

    (0)  (1)  (2)   (3)   (4)    .................................  (9)  (10)

    Because the question asks about odd number of elements so there are:

    \(10+120+252+120+10=512\left(subsets\right)\)

    ANSWER: 512 subsets

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  • ...
    Phạm Tuấn Đạt 11/11/2017 at 13:26

    We can do this by using Pascal's triangle. The numbers from the tenth row of the triangle (corresponds to the number in the subsets) is:

    1    10   45   120   210   252   210   120   45   10   1

    (0)  (1)  (2)   (3)   (4)    .................................  (9)  (10)

    Because the question asks about odd number of elements so there are:

    10+120+252+120+10=512( subsets)

    ANSWER: 512 subsets


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