You are studying a species of plants that has a wide geographic distribution, and have identified two true-breeding strains, both of which produce...

You are studying a species of plants that has a wide geographic distribution, and have identified two true-breeding strains, both of which produce plants that are 24 cm in height.  One strain came from Central America and the second from West Central Africa.  You cross the two strains and the F1 progeny are 24 cm in height.  However, when you allow the F1s to self fertilize, the heights of the F2 progeny range from 12 cm to 36 cm. 

a. What mode of inheritance is occurring?

b. Among the F2 progeny you find that approximately 1/250 are 12 cm and ~1/250 are 36 cm tall.  How many genes are involved in regulating height in this species? 

c. What are the probable genotypes of the true-breeding parents and the F1 progeny?

d. How much does each additive allele contribute to the height of the plant? 

e. What would you predict is/are the genotype(s) of members of this species that are 18 cm tall?

Hello

Mode of inheritance is polygenic Inheritance

I know my parents are going to be AAbbCCdd X aaBBccDD

My F1 is AaBbCcDd

36-12 = 24 cm

24 / 8 alleles = 3 cm per additive contributed

18 cm tall so 2 additive alleles. (12+3+3 = 18 cm)

I am confused on the Genotype portion. Am I suppose to do a binomial expansion???