Question

The letter of the word $RANDOM$ are written in all possible order and these are written out as in a dictionary then the rank if the word $RANDOM$ is

• A. $614$
• B. $615$
• C. $613$
• D. $616$

Answer 1

The correct option is A $614$

$RANDOM$

$\to$ Number of letters in RANDOM $\to 6$

$\to$ Number start with

$A{\to }^1{P}_1\times 5!=5\times 4\times 3\times 2\times 1=120$

$D{\to }^1{P}_1\times 5!=5\times 4\times 3\times 2\times 1=120$

$M{\to }^1{P}_1\times 5!=5\times 4\times 3\times 2\times 1=120$

$N{\to }^1{P}_1\times 5!=5\times 4\times 3\times 2\times 1=120$

$O{\to }^1{P}_1\times 5!=5\times 4\times 3\times 2\times 1=120$

RAD = $1\times 1\times 1\times 3!=3\times 2=6$

RAM = $1\times 1\times 1\times 3!=3\times 2=6$

RANDOM - 1

RANDOM -1

total no. of word = $120+120+120+120+120+6+6+1+1$

$=614$ words