Please show all work.

Will upvote if correct.

$1.$Given the following frequencies of letters appearing in a file, use Huffman Coding to determine the average number of bits used to encode a symbol, the binary code used to represent each bit, and the resulting binary tree.

A: $0\mathrm{.}08,$ B: $0\mathrm{.}10,$ C: $0\mathrm{.}12,$ D: $0\mathrm{.}15,$ E: $0\mathrm{.}20,$ F: $0\mathrm{.}35$