shortcut method is used when the lettors of the given word

This shortcut method is used when the lettors of the given word are not repeated.

Given word is MASTER

The letters of the are M,A,S,T,E,R.

Write the alphabetical order of the letters of the given word  MASTER  as A,E,M,R,S,T

Now strike off the first letter M.

A,E,M,R,S,T.

Then count the no.of letters before M, and it is equal to 2,which is the coefficient of 5!.

Again strike off the first letter A.

A,E,M,R,S,T

Then count the no.of letters before A and it is equal to 0 which is coefficient of 4!

Again strike off the first letter S.

A,E,M,R,S,T

Then count the no.of letters before S and it is equal to 2 which is coeffcient of 3!

Again strike off the first letter T.

A,E,M,R, S, T

Then count the no.of letters before T and it is equal to 2 which is coeffcient of 2!

Again strike off the first letter E.

A,E, M,R, S,T

Then count the no.of letters before E and it is equal to 0 which is coeffcient of 1!

Finally add 1 to the above values to get the rank of the word MASTER as follows:

2(5!) + 0(4!) +2(3!)+2(2!)+0(1!)+1=257