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To find the number of 2-number combinations that can be made with the numbers 1 through 6, we use the combination formula ( C(n, r) = \frac{n!}{r!(n-r)!} ), where ( n ) is the total number of items to choose from and ( r ) is the number of items to choose. Here, ( n = 6 ) and ( r = 2 ). Thus, the number of combinations is ( C(6, 2) = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15 ). Therefore, there are 15 different 2-number combinations that can be made with the numbers 1 to 6.

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