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MOHAMED KHALIFA MATHEMATICS INTRODUCTION: For mathematics, we were given the Coursework of investigating "Emma's Dilemma." This Coursework is set up in a number of steps which builds up to a formula in which one could enter any number of letters, with or without repeated letters, and come out with the number of possible permutations in which these words could be expressed. For this reason, I decided that I will not follow the steps and begin by investigating what is required, which is come up with the formula. I shall begin my task by looking at the possible number of ways in which I could write a word which has no letters repeated in it. I shall express the phrase "possible number of words" with the symbol ?. WORDS WITH NO REPEATED LETTERS: I shall start by looking at such words starting from single lettered words (Most of my words will not make sense): 1- ?...

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