So far, so good.
Having more than two sets of chromosomes is called polyploidy and it is most commonly found in plants. Triploids have three sets of chromosomes, tetraploids have four, etc.
acuminata) and the latter got the genome designation ‘BB’ (from balbisiana).
The formation of homogenomic triploids hybrids with the AAA genotype occurred within Musa acuminata, leading to cultivars that mostly comprise the sweet bananas. Crosses of the diploid and triploid types of Musa acuminata with Musa balbisiana resulted in the formation of heterogenomic triploid hybrids that are mostly plantains (AAB genotype) and other cooking bananas (ABB genotype). Tetraploid bananas do also exist.
The breeding of bananas needs triploids or tetraploids, rather than diploids, because only those result in virtually seedless bananas. The ‘Cavendish’ does so very rarely set seed that it is considered sterile. But it isn’t.
 Simmonds et al: The taxonomy and origins of the cultivated bananas in Journal of Linnean Society of London - 1955