How many ways are there to arrange the nine letter in the world ALLAHABAD?

HI, thanks for this wonderful stuff. I have a concern with last part of this question where you multiplied 1680 by saying both L can be arranged in two ways by themselves. Is it correct if both is the same word? Kindly reply if you really have started this forum for the visitors, not for the sake of "Link Building for search engines"

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Last updated at Sept. 3, 2021 by Teachoo

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Example 9 Find the number of permutations of the letters of the word ALLAHABAD. In ALLAHABAD There are 4A , 2L , 1H, 1B & 1D Since alphabets are repeating we will us this formula !/ 1! 2! 3! Total number of alphabets = 9 Here n = 9 , There are 4A s, 2L s hence taking p1 = 4 & p2 = 2 Hence total number of permutation = !/ 1! 2! = 9!/4!2! = (9 8 7 6 5 4!)/((2 1) 4!) = (9 8 7 6 5 )/2 = 7560