one allele (gene for the trait on the chromosome) from each parent gets passed down to the child. and brown eyes and brown/black hair is dominant. dominance/recessive doesn’t always occur though, there can also be co-dominance and mixing. there is a possibility but it depends on the genotype of the parents of father(1).

so in your example, the alleles for eyes are;

b(blue eyes)
B(brown eyes are dominant)

mother(1) – bb, you can only have blue eyes if you carry both rececive alleles.
father(1) – depending on what his parents genotypes are we cant really say. since his mother and father both have brown eyes they have to have the one B allele in both of their genotypes. yet either/both of them could be carrying a recessive b allele. this leaves the father with the possible combinations of Bb or BB for eye colour.

when mother(1) and father(1) have children the possible allele combinations for their children depending on the allele carried by the father and his parents are, Bb or bb. Mother(1) can only pass on a blue eye gene. father may pass on a brown/blue eyes gene, depending on what the genotype of his parents are.

it works the same way for the hair colour. as far as i can remember Red hair is dominant to Blonde, but Brown and Black hair is dominant to both red and blonde. so,

for mother(1)
red – R
blonde – r
since she has red hair we can deduce that she has Rr alleles, R from her mother and r from her father. since her father has blonde hair he has to have both rr alleles.

for father(1)
black – B
brown – b
and possibly blone
since his mother has brown hair it is possible that she is carrying a recessive blonde allele. it may be tricky determining the genotype with mixing and co-dominance between alleles being possible (among other things).
since he has black hair though he definately has a B allele. if he does infact have a child with blonde hair then the gene was most likely passed on from the mother or father of father(1)

so to answer your question, to find out a definitive possibility, we need to know where exactly that recessive blonde hair colour allele and the recessive blue eye colour allele came from on the father(1) side, ie did both grandparents have the recessive alleles or jus the grandmother or just the grandfather?

i did some calculations. i dont know if they are correct, but assuming the mother of mother(1) has both red hair alleles, and only the mother of father (1) carries the recessive blonde and blue eyes alleles, the possibility of mother(1) and father (1) having a blue eyes and blonde hair child is 3/64. that is if i calculated it correctly under those assumptions.

Are we assuming that hair color and eye color are controlled by one or several genes? In other words, do you want a realistic answer or an answer to a textbook question?