Question

find the rank of the word SYSTEM

Answer 1

first write word as EMSSTY
now E_ _ _ _ _ = 5!/2!
M _ _ _ _ _= 5!/2!
SE_ _ _ _ = 4!
SM_ _ _ _ = 4!
SS_ _ _ _= 4!
ST_ _ _ _=4!
SYE_ _ _=3!
SYM_ _ _=3!
SYSE_ _ =2!
SYSM_ _=2!
SYSTEM=1
rank= 60+60+24+24+24+6+6+2+2+1 = 209

Answer 2

Rank of a word – without repetition of letters

Suppose that you are given a word in which none of the letters are repeated and you asked to find out the rank of the word in a dictionary. For example, if the word which was given to you was CAT, it will be very easy to find out its rank. You will write down all possible combinations of the letters. Those are:

CAT, CTA, ATC, TCA, ACT, TAC

Now, you will arrange them in alphabetical order. It would become something like this:

ACT, ATC, CAT, CTA, TAC, TCA

CAT is third in the above list. So, the rank of the word CAT is 3.

But, as you might have realized by now – the problem would become extremely difficult if the word is bigger. Let us say that the word is SBIPO.

With just 5 letters, total possible arrangements are 5! or 120. It is not practical to write all of them down and find out the rank of the word SBIPO.