Question

If the letter of the word MOTHER are arranged in all possible orders and these words are written as in a dictionary, then the rank of the word MOTHER will be

• A. $240$
• B. $261$
• C. $308$
• D. $309$

Answer 1

The correct option is D $309$

To find rank of $MOTHER$

Total words starting from $E=5!=120$

Total words starting from $H=5!=120$

Number of words starting from $ME=4!=24$

Number of words starting from $MH=4!=24$

Number of words starting from $MOE=3!=6$

Number of words starting from $MOH=3!=6$

Number of words starting from $MOR=3!=6$

Number of words starting from $MOTE=2!=2$

Next word $=MOTHER$

Rank$=120+120+24+24+6+6+6+2+1$

$=309$