**Re: HSC 2016 MX2 Combinatorics Marathon**

Is this a question you are posing for others, or one you need help with?Consider an alphabet with n different available letters.

Let P(k) be the number of ways you can use exactly k different letters in an n letter word.

i) Explain why

ii) Show that

Let the Score of a word, X, be defined as 1/(1+#(X)), where #(X) is the number of letters that were not used by the word X.

iii) Show that the sum of all the Scores, S, over all possible n letter words, is given by:

iv) Hence, evaluate S in closed form.