Question

Determine the no. of genotype and phenotype produced in dihybrid ,trihybrid ,tetrahybrid ,and pentahybrid

Answer 1

Let the number of genes in the cross = n 
Dihybrid n=2 
trihybrid n=3 

There are two options for each allele so 2^n = gamete types, ie two alleles raised to the number of genes in the cross 
tetrahybrid has 2^4 = 16 gametes 

Next 2^2n = offspring, ie Two alleles raised to the # of genes x 2 for the # of parents 
tetrahybrid 2^2n = 2^8 = 256 offspring {this is also 16 gametes x 16 gametes} 

To calculate the number of genotypes it is 3^n 
tetrahybrid 3^n = 81 
look at pascal's triangle for the genotype ratios 
1:8:28:56:70:56:28:8:1 add these and get 256 
http://ptri1.tripod.com/ 
http://en.wikipedia.org/wiki/Pascal_tria... 
To find the chances of an offspring that is genotype AAbbCcDd 
is (1/4)x(1/4)x(1/2)x(1/2)=1/64 

In general the phenotype calculation is 
let m+n = number of genes in cross. So for a tetrahybrid cross with m+n = 4 
(3/4)^m x (1/4)^n 

(3/4)^4 x (1/4)^0 = 81/256 all genes are dominant phenotype 
(3/4)^3 x (1/4)^1 = (27/64)(1/4) = 27/256 [four times for all combinations] 
(3/4)^2 (1/4)^2 = (9/16)(1/16) = 9/256 [six times for all combinations] 

Phenotype ratio => 81:[27:27:27:27] : [ 9:9:9:9:9:9] : [3:3:3:3] :1 = 256

Answer 2

There is a handy formula to determine the number of genotypes;

3ⁿ [n = number of independent heterozygous gene pair]

In monohybrid cross, n = 1 ; thus no. of genotypes ⇒ 3¹ = 3

In dihybrid cross, n = 2 ; thus no. of genotypes ⇒ 3² = 9

In trihybrid cross, n = 3 ; thus no. of genotypes ⇒ 3³ = 27

In tetrahybrid cross, n = 4 ; thus no. of genotypes ⇒ 3⁴ = 81

In pentahybrid cross, n = 5 ; thus no. of genotypes ⇒ 3⁵ = 243

Thus, when the hetezygous pair increases, the number of genotype increases automatically.