Problem 1

Suppose you have the scrabble tiles 'A', 'D', 'E' and 'M'. Then there are 24 ways that you can arrange these tiles into strings of four letters (we'll call such a string a 'word'): ADEM, ADME, MDEA, DAME, EADM, MADE, .... (Some of these are words in English, many are not, but we count them all as words.) If you list all these words in alphabetical order then 'DAME' appears in the 8th place: ADEM, ADME, AEDM, AEMD, AMDE, AMED, DAEM, DAME ...

Now suppose that you have the ten scrabble tiles 'A', 'B', 'B', 'E', 'H', 'M', 'M', 'O', 'S', 'T'. If you were to arrange all possible words from these ten tiles in alphabetical order, in which place would 'MATHSBOMBE' appear? (If you think the answer is that MATHSBOMBE appears in the 12,345th place then you should enter 12345.)