Question

The letters of the word MODIVD are permuted and all the permutations are arrange in alphabetic order as in English dictionary. The number of words that appear before word MODIVD is

Answer 1

In a dictionary, letters in alphabetical order are $D,D,I,M,O,V$

So, the first word is $DDIMOV$

No. of words beginning with $D$ = No. of ways arranging $D,I,M,O,V$

$=5!=120$

The next word begin with $I$ and it is $IDDMOV$

No. of words beginning with $I$ = No. of ways arranging $D,D,M,O,V$

$=\frac{5!}{2!}=60$

The next word begin with $M$ and it is $MDDIOV$

No. of words beginning with $MD$ = No. of ways arranging $D,I,O,V$

$=4!=24$

No. of words beginning with $MI$ = No. of ways arranging $D,D,O,V$

$=\frac{4!}{2!}=12$

The next words begin with $MO$ and they are $MODDIV,MODDVI,MODIDV,MODIVD$

So, the number of words that appear before $MODIVD$ is $=120+60+24+12+3=219$