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5 choices for the first, 4 for the second .... so is 5x4x3x2x1 = 120 ways. If 2 of the letters are the same then for any arrangement, switching those 2 doesn't make any difference, so divide the answer by 2. If 3 are the same then there are 3x2x1 ways of shuffling those, which at first were all different arrangements but now are not, so divide by 3x2x1 ie 6.
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