The question https://mathoverflow.net/questions/173132/number-of-combinations-of-ordered-sequences-of-n-integers is closed because it is considered "undergraduate"... could someone explain me how in the world an undergraduate student will solve it? IMO, the solution does not involve simple Combinations and Permutations.
It does have an elementary solution, as I indicated in a comment that was discouraged by Andy Putman.
I will not tell you the worked out answer, and opinions here vary as to what contributes an answer. In any case , it is material that is covered in elememtary combinatorics texts, and is considered by me and many others as undergraduate level or earlier.
I would appreciate a remark from you, the OP on what is the best way to redirect you to math.SE, which is more appropriate. Did I say too much? Did I take too much of the process of learning away from you? Is Andy Putman right, and I should just say "go to math.SE"? I am interested in a candid response from you.