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Show that no compression scheme can expect to compress a file of randomly chosen 8-bit characters by even a single bit. In the hint, I

Show that no compression scheme can expect to compress a file of randomly chosen 8-bit characters by even a single bit.

In the hint, I am given that the number of possible source files S using n-bits and compressed files E using n-bits is 2^(N+1) - 1.

How can I prove this fact? Thanks you.

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