Question

The rank of the word MOTHER when the letters of the word are arranged alphabetically as in a dictionary, is

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ANSWER

(i) Arrange all the alphabets of word MOTHER in alphabetical order like [E, H, M, O, R, T]

Now, strike off the first letter M from [E, H, M, O, R, T]

Then count the no. of letter be fore M, and it is equal to 2, which 5!

Now, net word O,

Then, count the no. of letter before O and it is equal to 2, which is coefficient of 4!

Next letter T → 3!

Next letter H → 2!

and nett letter E → 1!

So, Rank of the word is

=2(5!)+2(4!)+3(3!)+1(2!)+0(1!)+1

=240+28+18+2+1

=309

word MOTHER is 309.