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There are 7 factorial, or 5040 permutations of the letters in the word NUMBERS.
three
7 factorial
239,500,800 12!/2! * * * * * Actually, as the word "permutation" [not permutations] has 11 letters, the answer is 11!/2! = 19,958,400
Since there are no duplicate letters in the word RAINBOW, the number of permutations of those letters is simply the number of permutations of 7 things taken 7 at a time, i.e. 7 factorial, which is 5040.