The letters of the word ‘HEXAGON’ are arranged in all possible ways. If the order of the vowels is not to be considered then the number of possible arrangements is

No of vowels$=3\left(E,A,O\right)$ 

Then the number of possible arrangements is $=\frac{7!}{3!}=840$       (  3 vowels order not to be consider )

( The number of permutations of ‘ n’  different things where order of ‘ r ’ things is not to be consider is = $\frac{n!}{r!}$)