Next-generation sequencing (NGS) offers a unique opportunity for high-throughput genomics and has potential to replace Sanger sequencing in many fields, including de-novo sequencing, re-sequencing, meta-genomics, and characterisation of infectious pathogens, such as viral quasispecies. Although methodologies and software for whole genome assembly and genome variation analysis have been developed and refined for NGS data, reconstructing a viral quasispecies using NGS data remains a challenge. This application would be useful for analysing intra-host evolutionary pathways in relation to immune responses and antiretroviral therapy exposures. Here we introduce a set of formulae for the combinatorial analysis of a quasispecies, given a NGS re-sequencing experiment and an algorithm for quasispecies reconstruction. We require that sequenced fragments are aligned against a reference genome, and that the reference genome is partitioned into a set of sliding windows (amplicons). The reconstruction algorithm is based on combinations of multinomial distributions and is designed to minimise the reconstruction of false variants, called in-silico recombinants.