probability of similarity of 4 digits from md5 hash of two strings

Question

Suppose we select four random digits from md5 hash of a string. And we select four random digits from md5 hash of some other string. What is the probability that these 4 digits will be same?

Answer 1

Some reasonable assumptions are in order:

  (1) Since nothing is said about "a string" and "some other string," we must assume that the MD5 hashes produced by them will have uniformly-distributed, random digits in the four positions that we select.

  (2) the "digits" mentioned in the problem are hexadecimal digits (0-F), not bits (0-1).

 

With these assumptions, the problem may be re-worded:

  Given a set of 16 digits, what is the probability of randomly selecting two groups of 4 digits that have the same 4 digits in them?  [notes:  repetition is permitted; now, you must determine whether order is important).