Hey confused_student, I found this site that may help you!
Problem 3.17 on page 63 asks you to use the forked-line method to determine the outcome of a number of trihybrid crosses.
Hint: In using the forked-line method, consider each gene pair separately. For example, in this problem, first predict the outcome of each cross for A/a genes, then for the B/b genes, and finally, for the C/c genes. Then you are prepared to pursue the outcome of each cross using the forked-line method.
In crosses involving two or more gene pairs, the calculation of gametes and genotypic and phenotypic results is quite complex. Several simple mathematical rules will enable you to check the accuracy of various steps required in working genetic problems.
First, you must determine the number of heterozygous gene pairs (n) involved in the cross. For example, where AaBb x AaBb represents the cross, n = 2; for AaBbCc x AaBbCc, n = 3; for AaBBCcDd x AaBBCcDd, n = 3 (because the B genes are not heterozygous). Once n is determined, 2n is the number of different gametes that can be formed by each parent; 3n is the number of different genotypes that result following fertilization; and 2n is the number of different phenotypes that are produced from these genotypes. Table 3.1 summarizes these rules, which may be applied to crosses involving any number of genes, provided that they assort independently from one another.
http://www.nicerweb.com/bio3400/Locked/qt/ebook/03_04.htmlFor classic dominant/recessive genes An elaboration...
let n = the number of heterozygous gene pairs of one parent
2 to the nth power = the number of different types of gametes produced
2 to the 2n power = # of offspring
for example, with a trihybrid cross, n = 3
# of gametes 2^3 = 8
# of offspring = 2^6 = 64
Trihybrid phenotypic ratio 27:9:9:9:3:3:3:1 = 64 offspring
A_B_C_ => (3/4)^3 (1/4)^0 = 27/64
A_B_cc => (3/4)^2 (1/4)^1 = 9/64 x3 positions
A_bbcc => (3/4)^1 (1/4)^2 = 3/64 x3 positions
aabbcc => (3/4)^0 (1/4)^3 = 1/64
3 to the nth power = the number of different genotypes produced
# of genotypes = 3^3 = 27
Trihybrid genotypic ratio 1:6:15:20:15:6:1 = 64 = 2^6
from polynomial expansion of (P+q)^6
P = dominant value for allele
q = recessive value for allele