We report results from two new methods for measuring the total production of charmed particles in nonresonant e+e- annihilations at s =10.5 GeV. The rate for detection of events containing two reconstructed charmed mesons relative to that for events containing one is used to extract information about total charm production independent of decay branching fractions. The value of Rcc», the total charm-pair cross section normalized to the pointlike -pair cross section, is found to be 1.13-0.13+0.17±0.09, under an assumption of limited particle correlations. In an independent analysis the inclusive cross section for e+e-qq»e±X is measured to be 0.293±0. 017±0.017 nb. Using measured relative production rates and semileptonic branching fractions of D0 and D+ mesons and estimates of these quantities for Ds and c, this is found to correspond to Rcc»=2.07±0.12±0.26. These two measurements are discussed in the context of measurements made by reconstruction of exclusive hadronic decay modes and of theoretical expectations.