Number of ways to arrange 4 digits such that there is at least one same pair

Question

For example

Not Accepted values: $4444$ (4444 is not a "pair"), $4040$, $4141$, $4440$ (444 is not a "pair").

Accepted values: $4400, 4401, 0440, 4404, 4004$

Digits may be $0-9$, not just 4 and 0 etc..

So far I've got ($1 - 10P4 - 10 $) which is (All - no repeating digits - all digits are the same). I've no idea how to go on with the other conditions. Perhaps my approach is wrong?

Answer 1

Hint:

Six possible forms: $$aabc, \quad baac, \quad bcaa$$ $$aaab, \quad baaa$$ $$aaaa$$ where $a,b$ and $c$ are pairwise distinct.

For the first three forms, we have $(10\times 9 \times 8) \times 3$ choices.

For the second row, we have $(10 \times 9) \times 2$ choices.

For the third row, we have $10$ choices.

In total, we have $2350$ choices from above. There are a couple of forms remaining. Can you finish?