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lets take a look at the following problem find the number of permutations of the letters of the word diploma for which the letter l remains in the middle position and how many ways are there to arrange the letters of the word diploma so that the letters o and i are together before i answer the two questions here first lets determine how many ways there are to arrange the letters of the word diploma without any conditions so diploma has six sorry seven letters so one two three four five six seven okay so if im rearranging the letters of this word first i have to check are there any repeated elements are all the letters unique the answer is yes so its time for me to fill out the first slot how many options do i have for this spot over here well there are seven letters so i have seven different letters to choose from for that spot once ive chosen a letter for that spot i have six options for the second spot five options for the third four options for the fourth three options two opt