In how many ways can the letters of the word SORTED be arranged to form different words of any length?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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Using the letters of the word SORTED, words can be formed of all lengths from 1 to 6.

The number of words of length n is equal to `P(6, n) = (6!)/((6 - n)!)`

Adding the number or words of all lengths that can be created gives:

`(6!)/(5!) + (6!)/(4!) + (6!)/(3!) + (6!)/(2!) + (6!)/(1!) + (6!)/(0!)`

=> 6 + 30 + 120 + 360 + 720 + 720

=> 1956

1956 words of any length can be formed using the letters of the word SORTED.

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