Question

Find the rank of the word MOTHER if all the words with letters of MOTHER are written in alphabetical order. .

Answer 1

The given word is MOTHER.

In a dictionary, the words are arranged in alphabetical order.

The words beginning with E, H, M, O, R and T are written in order.

Number of words starting with E = 5 = 120

Number of words starting with H = 5 = 120

Number of words starting with M = 5 = 120, but one of these words is MOTHER.

Now, number of words with ME = 4 = 24

Number of words with MH = 4 = 24

Number of words with MO = 4 = 24, but one of these words is MOTHER.

Now, number of words with MOE = 3 = 6

Number of words with MOH =3 = 6

Number of words with MOR = 3 = 6

Number of words with MOT =3 = 6, but one of these words is MOTHER.

The first word beginning with MOT is MOTEHR. The second word is

MOTERH. The third word is MOTHER.

Therefore, rank of MOTHER= 2(120) +2(24) +3(6) +3 =309