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    Combinatorial Mathematics : Distinct Elements and Combinations

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    5. Four numbers are selected from the set: {-5,-4,-3,-2,-1,1,2,3,4} . In how many ways can the selections be made so that the product of the numbers is positive and:

    a) The numbers are distinct.
    b) Each number may be selected as many as four times.
    c) Each number may be selected at most three times.

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    Solution Preview

    Let C(n,m)=n!/(m!*(n-m)!) be the combinatorial number.

    (a) All the 4 numbers are distinct and the their product is positive, then we can select 0 negatives and 4 positives, or 2 negatives and 2 positives, or 4 negatives and 0 positives. There are 5 negative number: -5, -4, -3, -2, -1 and 4 positive numbers 1, 2, 3, 4. Then the total number of ways is

    Solution Summary

    Distinct Elements and Combinations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.