Question

Find the number of distinguishable permutations of the letters in the word:TRIANGLE

Answer 1

40320

Step-by-step explanation:

In the word triangle, there are no repetition of of letters

`\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}`

This means the distinguishable permutation of the letters = (total number of letters)!

total number of letters = 8

the distinguishable permutation of the letters = 8!

`\begin{gathered} 8!\text{ = 8}*7*6*5*4*3*2*1 \\ 8!\text{ = 40320} \end{gathered}`

the distinguishable permutation of the letters = 40320