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If the four letters "A" are to be together, "AAAA", then it's like having four differentletters; AAAA, L, B, M.The number of different arrangements (permutations) of the 7 letters in the word"ALABAMA" putting the four As together are;4! =4x3x2x1 =24
There are 4 distinguishable letters in the word fish, so there is 4! or 24 different ways can you arrange the letters in the word fish.
Since you are using in the arrengement the all 4 letters, then there are 4! = 4*3*2*1 = 24 permutations.
Since the word MATH does not have any duplicated letters, the number of permutations of those letters is simply the number of permutations of 4 things taken 4 at a time, or 4 factorial, or 24.
There are 11!/(4!*4!*2!) = 34,650 ways.