The rank of the word $NUMBER$ obtained, if the letters of the word $NUMBER$ are written in all possible orders and these words are written out as in a dictionary is

The correct option is C $469$
Alphabetically,
Starting with B $5!$ ways
Starting with E $5!$ ways
Starting with M $5!$ ways
Starting with NB $4!$ ways
Starting with NE $4!$ ways
Starting with NM $4!$ ways
Starting with NU $4!$ ways
Starting with NUB $3!$ ways
Starting with NUE $3!$ ways
Starting with NUMBER $1!$ ways
Therefore, the total will be $3.5!+4.4!+2.3!+1=469$ ways
Hence, option 'B' is correct.