Section $1.$ There is only one answer per question for this section. A researcher studying hat color preference in holiday elves found a number of popular mutants that preferred green hats over the wildtype red hats. Thinking that the green hat genes might be advantageous in obtaining jobs at Williams and Sonoma during the holiday season the researcher went on to do a complementation analysis. The researcher was able to show that all mutant lines were true breeding and then did all of the pairwise crosses as shown below. Use the space provided to solve this problem and answer the ensuing questions. For consistence with the exam questions, use the following for possible gene annotations in order of identifying a gene; Gene $1-$ A$/$a$,$ Gene $2$ B$/$b$,$ Gene $3\frac{D}{d},$ Gene $4\frac{E}{e},$ Gene $5$ F$/$f and Gene $6\frac{G}{g}.$ Use subscripts $1,2,$ etc. to identify mutant alleles in order of their identification. R stands for Red, G stands for green and $P$ stands for Pink.

$\backslash$table$[[$Wildtype$,$Red,Genotype,Color,WT$,$M$1,$M$2,$M$3,$M$4,$M$5,$M$6],[$WT$,$R$,$R$,$R$,$R$,$R$,$R$,$G$],[$Mutant $2,$Green,,M$1,,$G$,$R$,$G$,$R$,$R$,$R$],[$Mutant $3,$Green,,M$2,,,$G$,$P$,$R$,$R$,$R$],[$Mutant $4,$Green,,M$3,,,,$G$,$R$,$R$,$R$],[$Mutant $5,$Green,,M$4,,,,,$G$,$P$,$R$],[$Mutant $6,$Green,,M$5,,,,,,$G$,$R$],[1.$ How,ge$,$d you,M$6,,,,,,,$G$]]$

B$.5,000$

C

D$.20,000$

E$.$ One

$4.$ Which of these is the best descriptor for the genotype for Mutant $4?$

A$.AA{b}_1{b}_1$DDEE

B$.a_2{a}_2$BBDDEE

C$.AA{b}_2{b}_2$DDEE

D$.AABBDD{e}_1{e}_1$

E$.AABB{d}_1{d}_{1}EE$

$5.$ Given the results in the table, which of the listed options is the best likely hypothesis about the expected ratio of green to red in the F$2$ from a mating of F$1$ kids from the cross of Mutant $2$ to Mutant $6?$

A$.0$:$4$

B$.1$:$1$

C$.13$:$3$

D$.4$:$0$

E$.15$:$1$

$6.$ Given the results in the table, which of the listed options is the best likely hypothesis about the expected ratio of green to red in the F$2$ from a mating of F$1$ kids from the cross of Mutant $4$ to Mutant $1?$

A$\mathrm{.}7$:$9$

B$.6$:$10$

C$.3$:$1$

D$.37$:$27$

E$.1$:$0$

$3.$ If these holiday elves genomes have exactly $20,000$ genes and there are no unknown$/$undiscovered genes hiding. We mean $20,000$ is all there is and don't try to imagine more. What is the minimum number of genes that could control hat color preference in wildtype holiday elves?

A$.$ Four