It would be worthwhile to read http://medicine.jrank.org/pages/2498/Meiosis-Sources-Genetic-Diversity.html. "A total of 2^23 (8.4 million) possible combinations of parental chromosomes can be produced by one person, and recombination further increases this to an almost unlimited number of genetically different gametes."
A good place to learn about how meiosis works is http://labs.russell.wisc.edu/peery/files/2011/12/Primer-in-Population-Genetics.pdf
Yes, mutation contributes to genetic diversity. But the main source of genetic variation for a small isolated population is the set of alleles available to the offspring of the initial population; and it is the multiplicity of chromosomes (plus crossover) that enables the shuffling of those alleles in producing those offspring.
For a definition of genetic diversity, see: UN (1992) Environment and Development (Terminology bulletin: 344). United Nations, New York, USA: "The variation in the amount of genetic information within and among individuals of a population, a species, an assemblage, or a community."
I should probably add that for the past 30 years I've been working with genetic algorithms, which are a software implementation of Darwinian evolution used for solving practical problems like stock portfolio optimization, machine design, and even for modeling biological evolution. The equivalent of chromosomes and crossover are, in most cases, unquestionably the key components that provide the genetic diversity necessary for finding "pretty good" solutions; while mutation is key to fine-tuning those "pretty good" solutions.
In biological evolution, chromosomes and crossover provide ways to make new combinations of alleles that are already available in the population; and mutation provides ways to create new alleles. Creation of new, useful alleles is a slow and uncertain process. Genetic recombination in meiosis involves the pairing of homologous chromosomes; crossover involves switching of blocks of genes between homologous chromosomes. In the short term (tens to hundreds of generations) those processes have vastly more adaptive potential than mutation. In the long term, other kinds of genetic rearrangement - and mutation - are necessary for big changes like creating new species.
The problem with the “standard” definition of genetic diversity is that, by that definition, it's possible for a large population to have genetic diversity of 1 and still contain only a handful of distinct genotypes. An environmental change could be a disaster, because the next generation would only have that handful of genotypes to select from regardless of the size of the population. But if the same set of alleles were randomly allocated throughout the population, every individual in the population could have a different genotype. In other words, genetic diversity according to the standard definition is not a reliable measure of the population's genetic resilience.
A better measure of the ability of a population to genetically adapt to changing selective pressures would be something that gauges how evenly the genotypes in the population are spread out over the space of possible genotypes. The maximally different hypothetical Adam and Eve would not constitute a genetically resilient population because they would represent only two genotypes. Not very many generations later, however, due to chromosomal recombination and crossover alone, without need for mutation, their descendants could comprise an extremely resilient population containing hundreds of thousands of distinct genotypes.