Multihoming has been broadly employed by large enterprises, and stub networks to augment the availability and reliability of their Internet access. In this technique, the edge network is connected to the Internet through multiple upstream Internet Service Providers (ISPs) rather than one. Thus far, different aspects of multihomed networks have received intensive attention in the research community. However, there have been quite a few works on the selection methodologies of upstream ISPs for a multihomed network which is definitely a primary prerequisite for other challenges in this area. In this paper, we try to address the ISP selection problem for provisioning of survivable end-to-end connections in multihomed networks. We first argue about different design decisions that the network operator has to make for support of resiliency against single-link network failures. Then, the minimum ISP selection problem is defined in which the goal is to pick the minimum number of upstream ISPs such that by multihoming to them, the major connections of the network would achieve a satisfactory level of resiliency against link failures. Then, we propose a brute-force method to optimally unravel this problem. Despite the NPhardness of our problem, we show that the proposed method can be used in practice to solve the problem in tolerable manner.