The word "BINARY" contains 6 unique letters. We aim to determine the count of distinct 4-letter sequences possible using these letters, with no letter appearing more than once. As the order of letter selection is significant for forming unique words, this scenario involves permutations.
A permutation signifies an ordered arrangement. The number of permutations when selecting \(r\) items from a set of \(n\) distinct items is calculated using the formula: \[ P(n, r) = \frac{n!}{(n-r)!} \]
In this context, \(n = 6\) (representing the letters B, I, N, A, R, Y) and \(r = 4\) (for the length of the words being formed).
Applying the formula: \[ P(6, 4) = \frac{6!}{(6-4)!} = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{2 \times 1} = 6 \times 5 \times 4 \times 3 \]
\[ = 360 \]
Consequently, 360 unique 4-letter words can be constructed from the letters of "BINARY" without repetition.