Question

If all the letters of the word $RANDOM$ are rearranged to form $6$ letter words and arranged in ascending order as in a dictionary, then the rank of the word $RANDOM$ is

• A. $614$
• B. $629$
• C. $601$
• D. $635$

Answer 1

The correct option is A $614$

Given word is $RANDOM$
Letters are $\{A,D,M,N,O,R\}$

The number of words starting with $A$ in the dictionary $=5!=120$
Similarly,
Number of word starting with $D$ is $120$
Number of word starting with $M$ is $120$
Number of word starting with $N$ is $120$
Number of word starting with $O$ is $120$
Next,
Word starting with $RAD$ is $3!=6$
Word starting with $RAM$ is $3!=6$
Then
$RANDMO$
$RANDOM$

$\therefore$ The rank of $RANDOM$ $=(120\times 5)+(6\times 2)+2=614$