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The text discusses finding the number of permutations of the word "diploma" where the letter "L" is in the middle position and arranging the letters so that "O" and "I" are together. It starts by determining the total number of ways to arrange the letters of "diploma" without any conditions, which is seven factorial. It then explains the process of filling out each slot with the available options, starting with seven options for the first slot, and decreasing by one for each subsequent slot.