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Abstract.Let n be a positive integer and suppose that each of {a"}J and (cs}J is an increasing sequence of nonnegative integers. Let M be the nxn matrix such that Afij=C(ai, c,), where C(m, ri) is the number of combinations of m objects taken nata time. We give an explicit formula for the determinant of M as a sum of nonnegative quantities. Further, if a,g:c,, ¡ = 1, 2, ■ ■ ■ , n, we show that the determinant of M is positive.