All 5! = 120 permutations of the word SMART are listed. What is the position of the word SMART?
+9519 OK, so the word "SMART" starts with S. We first want to know the approximate position of words that start with "S".
Arranging the letters in alphabetical order, we get "AMRST". That means words start with "S" is on a comparatively low position.
In reality, if we fix the first letter, there are 24 ways to arrange the other letters. So there are 24 words which start with "A", 24 which start with "M", so on and so on.
At the time we reach "S" finally, there would have been at least 72 words in front of the current word.
So the list of permutation looks like this:
AMRST
AMRTS
...
...
SAMRT
SAMTR
...
...
STRMA
...
...
So we need to know where does words which starts with "SM" lies.
When we fix the first two letters, there are 6 ways to arrange the other three.
So there are 72 + 6 words before the first word which starts with "SM".
And we also know that the first word which starts with "SM" is SMART, because "ART" is in alphabetical order.
Therefore, the position of the word is 72 + 6 + 1 = 79.
Edited: Sorry, I did basic arithmetic wrongly at the very last step.
