How many three letters arrangement are possible with the letters ANGLE if no letter may be repeated?

To find the number of three-letter arrangements possible with the letters in "ANGLE" without repeating any letters, we first note that there are 5 distinct letters: A, N, G, L, and E. For the first letter, we have 5 options, for the second letter 4 options (since one letter has already been used), and for the third letter, we have 3 options. Thus, the total number of arrangements is calculated as 5 × 4 × 3 = 60.