# Math Help - Permutations & Combinations

1. ## Permutations & Combinations

Q: Find out how many 3 figure numbers, lying between 100 and 999 inclusive, have 2 and only 2 consecutive figures identical.

Thank you for helping! ^^

You can choose $\frac{10!}{2! \cdot (10-2)!}$ sets of two numbers and you can permute them 2 times.
If you pick eg 2 and 9, you can make 992 and 229.
You need to consider that 0 and 1 can only make 100 so do -10 at the end.
I think you should get 80 numbers in the end.

3. ^ But the answer I was given is 162 numbers....