Question: 1. A dance company has ten members. How many different ways can a choreographer choose six dancers for a dance piece?
2. According to Dave Perkins, a chain reaction in the iPhone game Drop 7 can lead to scores of 7,39,109,224,391,617,... . Assuming this integer sequence continues in the fashion it started, what should the next number be?
3. Suppose that G has all vertices of degree 3. Prove that G can be decomposed into copies of K1,3 (a.k.a. claws), with vertices of different copies possibly overlapping, if and only if G is bipartite.