The DELPHI experiment at LEP has measured the inclusive charmless B hadron decay branching ratio, the B branching ratio into two charmed particles, and the total number of charmed particles per B decay, using the hadronic Z data taken between 1992 and 1995. The results are extracted from a fit to the b-tagging probability distribution based on the precise impact parameter measurements made using the microvertex detector. The inclusive charmless B branching ratio, including B decays into hidden charm (ccˉ), is measured to be 0.033±0.021. The B branching ratio into two open charmed particles is 0.136±0.042. The mean number of charmed particles per B decay (including hidden charm) is 1.147±0.041. After subtracting the B decay branching ratio into hidden charm, the charmless B branching ratio is found to be 0.007±0.021, compatible with the Standard Model expectation. Models that predict an additional contribution to the charmless B branching ratio of 0.037 or higher are excluded with at least 95\% confidence.