In this work, transmit antenna selection (TAS) and generalized selection combining (GSC), i.e., TAS/GSC is revised over independent identically distributed Nakagami-$m$ flat fading channels with pretty simple newly derived closed-form expressions of outage probability (OP), symbol error rate (SER), and ergodic capacity. While compares to their multinomial theorem-based counterparts for GSC and TAS/GSC, the intelligibility, practicality, and simplicity of our derivations are invaluable, which from now on facilitates TAS/GSC implementations in various fields. As an example, performance analysis of decode-and-forward multihop networks with TAS/GSC implementation in each hop is presented over independent non-identically distributed Nakagami-$m$ fading channels in this work, with the closed-form expressions for OP, SER, and ergodic capacity. Finally, all derived analytical expressions are validated via Monte-Carlo simulation technique.