This paper presents the first data-driven model for selecting carrier sentences with word and context embeddings. In computer-assisted language learning systems, fill-in-the-blank items help users review or learn new vocabulary. A crucial step in automatic generation of fill-in-the-blank items is the selection of carrier sentences that illustrate the usage and meaning of the target word. Previous approaches for carrier sentence selection have mostly relied on features related to sentence length, vocabulary difficulty and word association strength. We train a statistical classifier on a large-scale, automatically constructed corpus of sample carrier sentences for learning Chinese as a foreign language, and use it to predict the suitability of a candidate carrier sentence for a target word. Human evaluation shows that our approach leads to substantial improvement over a word co-occurrence heuristic, and that context embeddings further enhance selection performance.