Consider a ribosome translating a codon to an amino acid. Compared to a perfect pairing, imagine that a codon-anticodon paring with one incorrect base pair is 10 kJ/mol higher in energy, two incorrect base pairs is 20 kJ/mol higher, and three incorrect base pairs is 30 kJ/mol higher.

How many ways are there of making a one-, two-, or three-base-pair mismatch? What is the partition function of the codon-anticodon system at 300 K? If energy difference is the only consideration, what percent of decoding events occur with an error (no mismatches) at 300 K?