Final answer:
There are 120 permutations of the word "triangle" where "t" and "e" hold the last positions, which is calculated by finding the factorial of the remaining 5 letters (5!).
Step-by-step explanation:
To find out how many permutations can be formed with the letters in "triangle" where "t" and "e" occupy the last positions, we have to consider how many different ways the remaining letters can be arranged. There are 7 letters in the word "triangle," but since "t" and "e" are fixed at the end, we have 5 letters to arrange ("r," "i," "a," "n," "g"). The number of permutations of these 5 letters is 5 factorial (5!).
5 factorial (5!) is calculated as 5 x 4 x 3 x 2 x 1, which equals 120. Therefore, there are 120 permutations of the word "triangle" where "t" and "e" are in the last positions.