Does $\pi$ contain all possible number combinations?

It is not true that an infinite, non-repeating decimal must contain ‘every possible number combination’. The decimal $0.011000111100000111111\dots$ is an easy counterexample. However, if the decimal expansion of $\pi$ contains every possible finite string of digits, which seems quite likely, then the rest of the statement is indeed correct. Of course, in that case it also contains numerical equivalents of every book that will never be written, among other things.

Let me summarize the things that have been said which are true and add one more thing.

1. $\pi$ is not known to have this property, but it is expected to be true.
2. This property does not follow from the fact that the decimal expansion of $\pi$ is infinite and does not repeat.

The one more thing is the following. The assertion that the answer to every question you could possibly want to ask is contained somewhere in the digits of $\pi$ may be true, but it's useless. Here is a string which may make this point clearer: just string together every possible sentence in English, first by length and then by alphabetical order. The resulting string contains the answer to every question you could possibly want to ask, but

• most of what it contains is garbage,
• you have no way of knowing what is and isn't garbage a priori, and
• the only way to refer to a part of the string that isn't garbage is to describe its position in the string, and the bits required to do this themselves constitute a (terrible) encoding of the string. So finding this location is exactly as hard as finding the string itself (that is, finding the answer to whatever question you wanted to ask).

In other words, a string which contains everything contains nothing. Useful communication is useful because of what it does not contain.

You should keep all of the above in mind and then read Jorge Luis Borges' The Library of Babel. (A library which contains every book contains no books.)

It is widely believed that $\pi$ is a normal number. This (or even the weaker property of being disjunctive) implies that every possible string occurs somewhere in its expansion.

So yes, it has the story of your life -- but it also has many false stories, many subtly wrong statements, and lots of gibberish.