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.