Math, asked by nillu0, 1 year ago

 if letters of word 'MOTHER' are written in all possible orders and these words are written out as in dictionary find the rank pof the word 'MOTHER'.​

Answers

Answered by ranjanalok961
56

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

Answered by ssvijay738
18

There are 6 letters and all are different.

In dictionary, words starting from E, H will come before word MOTHER.

so, total no. of words starting from E = 5!= 120

(we have to arrange 5 letters on five places)

similarly, no. of words starting from H = 5! = 120

now, first word starting with letter M will come..

similarly, no. of words starting with ME.... = 4!

no. of words starting with MH.... = 4!

now, words starting from MO will come

no. of words starting with MOE... =3!

no. of words starting with MOH... =3!

no. of words starting with MOR... =3!

now, words starting from MOT will come

no. of 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 in dictionary = 307

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