Find the word at $48$ position? 
The letters in the word "PLACES" are permuted in all possible ways and arranged in the alphabetical order.Find the word at 48 position.

a)AESPCL
b)ALCEPS
c)ALSCEP
d)AESPLC
MyApproach
As per dictionary I started with 
AC--->$4$!=$24$
AE--->$4$!=$24$
So,I think the word start with AE but I am confused which to choose.

Am I right in my approach.Please correct me if I am wrong?

 A: The approach is correct.
As there will be 24 words starting with AE, the 48th will be the last one starting with AE i.e. AE-S-P-L-C.
I hope that makes sense.
A: First, use the Factorial Number System in order to calculate $47_6$ as follows:


*

*$47/5!=5!\cdot\color\red0+47$

*$47/4!=4!\cdot\color\red1+23$

*$23/3!=3!\cdot\color\red3+ 5$

*$ 5/2!=2!\cdot\color\red2+ 1$

*$ 1/1!=1!\cdot\color\red1+ 0$

*$ 0/0!=0!\cdot\color\red0+ 0$


Then, take the resulting string of $\color\red{013210}$, and run the following algorithm:


*

*$\color\red013210,\color\red{A}CELPS$

*$\color\red13210,C\color\red{E}LPS$

*$\color\red3210,CLP\color\red{S}$

*$\color\red210,CL\color\red{P}$

*$\color\red10,C\color\red{L}$

*$\color\red0,\color\red{C}$


The result is $\color\red{AESPLC}$.
A: AESP is fixed as you have 2 options you got by finding rank . IN DICTIONARY  AESPCL will be 47 th word while AESPLC will be 48 th as alphabetically L comes after C . Hence option D.
A: word is  "PLACES"
Arrange this in alphabetical order like ACELPS
fixing AC---- we had remaining 4 letters we can arrange them in 4! ways
1st word is AC (ELPS)
4! ways means (4*3*2*1=24) In 24 ways we can arrange those 4 letters(ELPS)
To get 24th word just revers the remaining  4 letters
like  AC ELPS  as  AC SPLE
we had 24th word  as ACSPLE 
But we need 48th word  so again fix AE---- Remaining 4 letters in 4! ways  
To get 48th word just revers the remaining  4 letters
like  AE CLPS  as  AE SPLC
Therefore  48th word  is AESPLC 
