Exported Activity (EA), a kind of activities in Android apps that can be launched by external components, is one of the most important inter-component communication (ICC) mechanisms. In combinatorial testing of EAs, although exhaustive testing of all possible combinations of input elements is ideal, it is often not feasible due to the combinatorial explosion of test cases. This paper presents ExaDroid, a novel variable-strength combinatorial testing framework for generating test suites for exported activities. ExaDroid is based on two observations: many activities are unintentionally exposed, and the complexity of input interactions in activities can be very limited. ExaDroid uses misexposure prediction and complexity analysis to decide the (default) testing strength of an EA. It also leverages input interactions to focus testing resources on important combinations by setting stronger (variable) test strengths on certain attributes. Our experiments have confirmed that ExaDroid is capable of trigger many unique crashes using a dozen or so test cases. The tool successfully found 100 unique crashes across 135 EAs in 30 apps, at an average cost of 14.2 test cases per EA.