How many five digit numbers are there which have first three digits in ascending order and last three digits in descending order? I thought people from all faculty can ponder on this, that is why I placed it in GD rather than Maths forum. Clarifications (Added after 6 replys had been made): 1. Base 10. (Never thought I would have to answer this too!) 2. strictly ascending and strictly descending. 3. No leading 0s allowed. But since this isn't a home-work question It doesn't really much matter what assumptions you take. I just wanted to see how you would approach it. But the assumptions shouldn't make it too easy, like assuming, Base 2, not-strictly ascending, and No leading 0s.