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Combinatorial Mathematics : Distinct Elements and Combinations

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.

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

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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.