In this paper, we develop a very simple mathematical model to investigate the upper bound of the size of limited choices in our proposed QoS path selection algorithm called the Largest Widest Shortest Path among Limited Choices (LWSP-LC) for engineering design. The LWSP-LC can achieve load balancing effectively and reduce path searching complexity significantly. However, its performance is highly related to many factors including the network environment and traffic condition. Our simulation results show that the size of limited choices is highly dependent on both the network size and network connectivity. By considering a fully connected network, we derive a simple mathematical model on the upper bound of the size of limited choices based on the network size only.