Question from Cambridge STEP Paper.

Hi everyone, I was looking through STEP Papers because I'm considering doing Mathematics at University. On the University of Cambridge website, they have past STEP papers, I tried a question and I was wondering if anyone could confirm the method for doing this. The question was:

How many integers between 10 000 and 100 000 (inclusive) contain exactly 2 different digits? (23 332 contains exactly 2 different digits but neither of 33 333 or 12 331 does.)

My calculation gave me an answer of 1 217.

Can someone try this question and let me know what they got and how they got it?

I'll explain my method too after there has been confirmation of whether my answer is right or wrong.