From the letters of the word 'BRIGHT', how many distinct $3$ -letter word arrangements can be formed without repeating any letter?

The word 'BRIGHT' contains $6$ letters: B, R, I, G, H, T. All $6$ letters are unique.
We need to find the number of arrangements of taking $3$ letters at a time out of these $6$ distinct options without repetition. This is calculated using the permutation formula ${}^n{P}_r$:

$${}^6{P}_3=\frac{6!}{(6-3)!}=\frac{6!}{3!}=6\times 5\times 4=120$$

Thus, $120$ distinct $3$ -letter arrangements can be formed.