Question

question
what is the total number of different 12-letter arrangements that can be formed using the letters in the word trigonometry?
answer attempt 1 out of 2

Explanation:

Step1: Count total letters

The word TRIGONOMETRY has 12 letters.

Step2: Identify repeated letters

Letters: T(2), R(2), I(1), G(2), O(2), N(1), M(1), E(1), Y(1). Repeats: T(2), R(2), G(2), O(2).

Step3: Apply permutation formula

Formula for permutations of multiset: $\frac{n!}{n_1!n_2!...n_k!}$ where $n=12$, $n_1=n_2=n_3=n_4=2$.
$$\frac{12!}{2!2!2!2!}$$

Step4: Calculate the value

$12! = 479001600$, $2!^4 = 16$. So $\frac{479001600}{16} = 29937600$.

Answer:

29937600