Final answer:
An alligator's body cells contain 64 chromosomes, as its sex cells or gametes have 32 chromosomes; body cells have twice the number of chromosomes than gametes.
Step-by-step explanation:
Alligators have diploid cells, meaning their body cells contain two sets of chromosomes, one set inherited from each parent. The question states that an alligator has 32 chromosomes in its sex cells, which are gametes. In sexually reproducing eukaryotic organisms, gametes are haploid, having half the number of chromosomes found in diploid body cells. Therefore, if an alligator's gametes have 32 chromosomes, its body cells would have twice that number.
Thus, the correct answer to the question 'An alligator has 32 chromosomes in its sex cells. How many chromosomes are in its body cells?' is Option 1: 64 chromosomes.