Why are 3 nucleotides used as codons for amino-acid mapping in dna?

This is because it is the code language that tRNA uses  during the process of translation.

In the cell, DNA has the genetic code for proteins needed for the cell to be able to function. To be able to make a particular protein, the code for that protein, which  can be compared to a blue print has to be delivered from the DNA to the ribosome which can be compared to a work shop for it is here that amino acids, the building blocks of protein, are put together to form the protein.

In the cell nucleus, DNA transcribes (copies) the blue print on to mRNA, which then leaves the nucleus and carries the blue print  to the ribosomes in the cell cytoplasm and attaches to a ribosome. tRNA begins to translate or read the information on the attached  mRNA in triplets or codons and not as single nucleotides.  Each codon is a code for a specific amino acid.  tRNA then fetches amino acids (coded for by each codon) from the pool of free amino acids in the cytoplasm and brings them to the ribosome where they are joined to each other to form a chain thus  creating the protein.

the answer to your question is b