Wanna' check the pollination results?  Count the seeds.
  You'll find the best quality apples have 7-10 seeds, if you slice them crosswise and count 'em. There are five seed pockets with two possible seeds in each one. Count only brown, plump seeds, white or shrivelled ones don't count.

  Apples with less than 3 seeds usually go down in the June drop, those with 3-4 seeds tend to make unprofitable and starchy bag apples, those from 5-7 seeds are, of course, in between. The seed count affects the size and shape of the apple, as well as the conversion of starch to sugar (ripening). If you wait long enough, the 3 seeded, starchy apples will finally ripen, but they will often get mealy, before the sugar content is up where it should be for good taste.

  Pollination is dependent on good pollenizer varieties, enough healthy bees, and favorable weather conditions. A grain of compatible pollen is needed for each seed, and that doesn't usually occur with one bee visit. We want to get the bee into the blossom many times.

  For lots more info on pollenizers, pollinators, and pollination:

The Pollination Home Page
http://pollinator.com

Pollenizers in a Drum

  Bouquets of crab apple blossoms are set in the orchard to provide viable pollen for the main crop apples.

Cross sectional drawing of the structure of the apple flower. From McGregor: Insect Pollination of Cultivated Crop Plants  USDA, 1976