Why are Huffman codes, calculated from the same probabilities, not unique? (That is, how can there be multiple different sets of code words that achieve the same thing?)Question 1Select one or more:The allocation of 0 to one path and 1 to the other, when generating the code words in the Huffman tree, is arbitrary.The probabilities do not influence the selection of Huffman code wordsProvided the set of code words are of variable length as calculated by the algorithm, it does not matter which code word is allocated to which symbol.If some symbol probabilities, or grouped symbol probabilities are the same, then the choice of which are combined is arbitraryHuffman code words are always n bits long to cover 2n symbols, so there allocation to particular symbols is arbitrary.

The Huffman codes calculated from the same probabilities are not unique due to the following reasons:

1. The allocation of 0 to one path and 1 to the other, when generating the code words in the Huffman tree, is arbitrary. This means that you could start with 0 or 1, and the resulting Huffman codes would still be valid and achieve the same compression efficiency.

2. If some symbol probabilities, or grouped symbol probabilities are the same, then the choice of which are combined is arbitrary. This means that if two symbols have the same probability, you could choose either one to combine first when building the Huffman tree. This would result in different Huffman codes, but they would still have the same length and thus the same compression efficiency.

3. Provided the set of code words are of variable length as calculated by the algorithm, it does not matter which code word is allocated to which symbol. This means that as long as the code words are of the correct length, the specific allocation of code words to symbols does not affect the compression efficiency.

The other two options are incorrect. The probabilities do influence the selection of Huffman code words, as symbols with higher probabilities get shorter code words. Also, Huffman code words are not always n bits long to cover 2n symbols, they are of variable length depending on the symbol probabilities.