In the cross between smooth seed coat and wrinkled seed coat, all F1 generation seeds had a smooth coat. Determine the genotypes of the F1 generation and the F2 genotypic ratio.

In the cross between smooth seed coat and wrinkled seed coat, all F$_1$ generation seeds had a smooth coat. This indicates that the smooth seed coat trait is dominant over the wrinkled seed coat trait.

Let 'S' represent the dominant allele for smooth seed coat.
Let 's' represent the recessive allele for wrinkled seed coat.

Since all F$_1$ offspring are smooth, the smooth parent must be homozygous dominant (SS) and the wrinkled parent must be homozygous recessive (ss).
Parental genotypes: Smooth (SS) $\times$ Wrinkled (ss)

a) Work out the genotypes of the F$_1$ generation.
To find the F$_1$ genotypes, we cross the parental genotypes:

$$\text{P: SS} \times \text{ss}$$

Gametes: S from SS, s from ss

$$\text{F}_1: \text{Ss}$$

All F$_1$ individuals are heterozygous (Ss) and will express the dominant smooth phenotype.

The genotypes of the F$_1$ generation are: $\boxed{\text{Ss}}$

b) From the information above, work out the following for the F$_2$ generation:
The F$_1$ generation (Ss) was selfed. This means we cross Ss $\times$ Ss.

We can use a Punnett square:

	S	s
S	SS	Ss
s	Ss	ss

b) (i) Genotypic ratio for the F$_2$ generation.
From the Punnett square, the genotypes are SS, Ss, and ss.
The ratio of these genotypes is:

$$\text{SS : Ss : ss} = 1 : 2 : 1$$

The genotypic ratio is: $\boxed{1:2:1}$

b) (ii) The total number of wrinkled seeds in the F$_2$ generation.
From the Punnett square, the genotype 'ss' corresponds to the wrinkled seed phenotype.
The proportion of 'ss' individuals in the F$_2$ generation is $\frac{1}{4}$.
The total number of F$_2$ generation individuals is 7324.

Number of wrinkled seeds = (Proportion of wrinkled seeds) $\times$ (Total F$_2$ individuals)

$$\text{Number of wrinkled seeds} = \frac{1}{4} \times 7324$$ $$\text{Number of wrinkled seeds} = 1831$$

The total number of wrinkled seeds is: $\boxed{1831}$

b) (iii) Phenotypic ratio for the F$_2$ generation.
From the Punnett square:

• SS and Ss genotypes result in the smooth phenotype (dominant).
• ss genotype results in the wrinkled phenotype (recessive).

So, the phenotypes are Smooth (SS, Ss) and Wrinkled (ss).
The ratio of these phenotypes is:

$$\text{Smooth : Wrinkled} = (1+2) : 1 = 3 : 1$$

The phenotypic ratio is: $\boxed{3:1}$