Question

In how many different ways can you arrange the letters of the word TRIGONOMETRY?

Answer 1

The number of arrangements will depend upon how many duplicate letters are present. List the letters and the number of duplicates:

Explanation:

T - 2
R - 2
I - 1
G - 1
O - 2
N - 1
M - 1
E - 1
Y - 1

So, there are 12 letters total , with T, R and O having duplicates.

arrangements `=(12!)/(2!xx2!xx1!xx1!xx2!xx1!xx1!xx1!xx1!)`

`=59,875,200` arrangements

hope that helped