Answer :
40320
Explanation:In the word triangle, there are no repetition of of letters
[tex]\begin{gathered} \text{If there are repetition in letters:} \\ \text{distinguishable }permutation\text{ = }\frac{(total\text{ number of words in the letter)!}}{(\text{each repetition)!}} \end{gathered}[/tex]This means the distinguishable permutation of the letters = (total number of letters)!
total number of letters = 8
the distinguishable permutation of the letters = 8!
[tex]\begin{gathered} 8!\text{ = 8}\times7\times6\times5\times4\times3\times2\times1 \\ 8!\text{ = 40320} \end{gathered}[/tex]the distinguishable permutation of the letters = 40320