Question

question
what is the total number of different 9-letter arrangements that can be formed using the letters in the word rearrange?
answer attempt 2 out of 2

Explanation:

Step1: Count total letters and duplicates

Total letters: 9. Duplicates: R(3), A(2), E(2), N(1), G(1).

Step2: Apply permutation formula for duplicates

Formula: $\frac{n!}{n_1!n_2!...n_k!}$ where $n=9$, $n_R=3$, $n_A=2$, $n_E=2$.

Step3: Calculate factorial values

$9! = 362880$, $3! = 6$, $2! = 2$, $2! = 2$.

Step4: Compute the result

$\frac{362880}{6×2×2} = \frac{362880}{24} = 15120$.

Answer:

15120