Dynamic web service selection refers to determining a subset of component web services to be invoked so as to orchestrate a composite web service. Previous work in web service selection usually assumes the invocations of web service operations to be independent of one another. This assumption however does not hold in practice as both the composite and component web services often impose some orderings on the invocation of their operations. Such orderings constrain the selection of component web services to orchestrate the composite web service. We therefore propose to use finite state machine (FSM) to model the invocation order of web service operations. We define a measure, called aggregated reliability, to measure the probability that a given state in the composite web service will lead to successful execution in the context where each component web service may fail with some probability. We show that the computation of aggregated reliabilities is equivalent to eigenvector computation. The power method is hence adopted to efficiently derive aggregated reliabilities. In orchestrating a composite web service, we propose two strategies to select component web services that are likely to successfully complete the execution of a given sequence of operations. Our experiments on a synthetically generated set of web service operation execution sequences show that our proposed strategies perform better than the baseline random selection strategy.