This paper describes new measurements from CLEO of the inclusive B→Ds+X branching fraction as well as the B+→Ds(*)+D¯(*)0 and B0→Ds(*)+D(*)− branching fractions. The inclusive branching fraction is B(B→Ds+X)=(12.11±0.39±0.88±1.38)% where the first error is statistical, the second is the systematic error, and the third is the error due to the uncertainty in the Ds+→φπ+ branching fraction. The branching fractions for the B→Ds(*)+D¯(*) modes are found to be between 0.9% and 2.4% and are significantly more precise than previous measurements. The sum of the B→Ds(*)+D¯(*) branching fractions is consistent with the results of fits to the inclusive Ds+ momentum spectrum. Factorization is used to arrive at a value for fDs, the Ds+ decay constant. © 1996 The American Physical Society.