Size in not relevant. Apples have five seed pockets or carpels. Each pocket contains seeds. The number of seeds per carpel is determined by the vigor and health of the plant. Different varieties of apples will have different number of seeds.
This sounds like a good science experiment. You have a great answer from the expert, but what have you actually gained through experience for your child? I would purchase a few apples in different varieties and sizes, cut them open and count recording my findings. Also, it's fun to cut the apple in 1/2 horizontally to find the star inside.
I've included a link to an education.com science experiment that you may want to do while you're working these apples (just add to the fun).
This is a great question that can be investigated at home, in the lab, or in the field!
The number of seeds depends on the variety of apple you have. While there are five seed-containing sections (carpels) in all apples, an apple may produce anywhere from 0-20 plus seeds. Is not just genetics, but how well the growing season went also affects the number of seeds.
For some varieties, size matters! A red delicious apple that is small almost always has fewer seeds than a red delicious that is large (Fancy Grade). The small apple has fewer resources to sustain seed development.
For learners with a scientific curiosity, check out the data for Granny Smith, Honey Crisp, and Red Delicious apples.