6

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?

justin takro
  • 1,288

4 Answers4

2

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.

Amit Saxena
  • 358
2

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 $\color\red{AESPLC}$.

barak manos
  • 43,109
0

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.

Archis Welankar
  • 15,910
0

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

sai ram
  • 1