The letters of the word $BRONZE$ are written in all possible orders. How many words are possible? If these words are written out in a dictionary what is the rank of the word $BRONZE$?

No. of words starting with $BE=4!$ (RONZ arranged)

Similarly words starting with $BN=4!$

$BO=4!$

Then comes $BR$

Now words starting with $BRE=3!$

$BRN=3!$

They comes $BRO$

Words starting with $BROE=2!$

Words starting with $BRONE=1$

Then come $BRONZE$, the required word

$\therefore RANK=4!+4!+4!+3!+3!+2!+2!+1+1$

$=72+12+2+2$

$\therefore RANK=86$

$\therefore$ Rank is $86$