The Greatest Combinatorics

AGREATESTMATH contains 13 letters of which 8 are consonants and 5 vowels. First lets arrange the consonants by $\dfrac{8!}{3!}$ (T repeats 3 times). Now, there are (8 + 1 = 9) places amde by these 8 consonants.And we have to arrange 5 vowels in them. Now, choose 5 places by $\dbinom{9}{5}$ . Now, arrange them by $\dfrac{5!}{2! × 3!}$ (A repeats thrice and E repeats twice). So, our final answer is $\dfrac{8!}{3!} × \dbinom{9}{5} × \dfrac{5!}{2! × 3!} = \color{#3D99F6}{\boxed{8467200}}$ .