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Determine the number of ways to arrange the letters of the word PROOF.

 Sep 19, 2020
 #1
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P R O O F =5! / 2! = 60 Permutations as follows:

 

{F, O, O, P, R} | {F, O, O, R, P} | {F, O, P, O, R} | {F, O, P, R, O} | {F, O, R, O, P} | {F, O, R, P, O} | {F, P, O, O, R} | {F, P, O, R, O} | {F, P, R, O, O} | {F, R, O, O, P} | {F, R, O, P, O} | {F, R, P, O, O} | {O, F, O, P, R} | {O, F, O, R, P} | {O, F, P, O, R} | {O, F, P, R, O} | {O, F, R, O, P} | {O, F, R, P, O} | {O, O, F, P, R} | {O, O, F, R, P} | {O, O, P, F, R} | {O, O, P, R, F} | {O, O, R, F, P} | {O, O, R, P, F} | {O, P, F, O, R} | {O, P, F, R, O} | {O, P, O, F, R} | {O, P, O, R, F} | {O, P, R, F, O} | {O, P, R, O, F} | {O, R, F, O, P} | {O, R, F, P, O} | {O, R, O, F, P} | {O, R, O, P, F} | {O, R, P, F, O} | {O, R, P, O, F} | {P, F, O, O, R} | {P, F, O, R, O} | {P, F, R, O, O} | {P, O, F, O, R} | {P, O, F, R, O} | {P, O, O, F, R} | {P, O, O, R, F} | {P, O, R, F, O} | {P, O, R, O, F} | {P, R, F, O, O} | {P, R, O, F, O} | {P, R, O, O, F} | {R, F, O, O, P} | {R, F, O, P, O} | {R, F, P, O, O} | {R, O, F, O, P} | {R, O, F, P, O} | {R, O, O, F, P} | {R, O, O, P, F} | {R, O, P, F, O} | {R, O, P, O, F} | {R, P, F, O, O} | {R, P, O, F, O} | {R, P, O, O, F} (total: 60)

 Sep 19, 2020

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