To know the possible number of genetical difference eggs you can have, you need to do
2^number of heterozygotes
If you have a B C D E x a b c D e = aa Bb Cc DD Ee
You have three heterozygotes. You have 2^3=8 possibilities.
The probability of producing a child that will phenotypically resemble either one of the two parents is the possibility of having each gene.
1/2 of B and 1/2 of b
1/2 of C and 1/2 of c
1/2 of E and 1/2 of e
1/1 a
1/1 D