Due to chromosome crossover, you do not inherit genes individually from ancestors, but instead you inherit segments of chromosomes containing many genes.

However, the randomness is great enough that first cousins do share approximately 1/8 of their genes, second cousins 1/32, third cousins 1/128 and so on. The rapid decrease of shared genes among relatives in successive generations also means that if mating in a population is really random, the population rapidly becomes homogeneous.

It is only assortative mating which generates and maintains distinctive subpopulations.