Question

If the letter of the word Mother are written in all possible orders and these words are written out as in a dictionary, then the rank of the word Mother is ?

• A. $307$
• B. $261$
• C. $308$
• D. $309$

Answer 1

Answer: (A)

$307$

There are 6 letters, each different

Before MOTHER, words from E , H will come

Words from E = 5! (there are 5 letters to arrange)

Words from H = 5!( there are 5 letters to arrange)

Now words starting by M will come.

First ME will have = 4! (as 4 letters will be arranged)

Then MH = 4!

Now words with MO

First words starting with MOE... =3!

And words starting with MOH... =3!

the words starting with MOR... =3!

Now, words starting from MOT will come

words starting with MOTE.. = 2!

then after words starting from MOTH will come and first word will MOTHER

so, total no. of words before MOTHER = 5! + 5! + 2* 4! + 3 * 3!

= 120 +120 + 48 + 18

= 306

so, rank of MOTHER = 307