Final answer:
Using permutations, 720 different 'words' can be formed from 'TRUMPS,' and 180 from 'TEETER' considering repeated letters, by applying the formula 6! for 'TRUMPS' and 6!/(2!x2!) for 'TEETER'.
Step-by-step explanation:
To determine how many different “words” can be formed by using all the letters of the word 'TRUMPS' exactly once, we calculate the factorial of the number of letters in the word. Since 'TRUMPS' has 6 unique letters, the number of different permutations is 6!, which is equal to 6×5×4×3×2×1 = 720 possible arrangements.
In the case of the word 'TEETER,' we must consider the repetitions of the letters. 'TEETER' has 2 'E's and 2 'T's. The total number of letters is 6, so we initially have 6! arrangements. However, to account for the repetition, we divide by the factorial of the number of each repeated letter (2 'E's and 2 'T's), resulting in 6! / (2!×2!) = 720 / (2×2) = 180 different “words”.