1. If the different permutations of the word PROGIDIOUS are listed as in a dictionary, then what is the rank of the word PROGIDIOUS?
Solution:
PROGIDIOUS
Arrange the letter in order D,G,I,I,O,O,P,R,S,U
Words begins with Arrangement of words
D 9!/2!x2!
Hint: (total nine letters with repeating letter)
G 9!/2!x2!
I 9!/2!
O 9!/2!
PD 8!/2!x2!
PG 8!/2!x2!
PI 8!/2!
PO 8!/2!
PRD 7!/2!x2!
PRG 7!/2!x2!
PRI 7!/2!
PRODG 5!/2!
Next two words remaining as arranged accordingly
PROGIDIOSU and PRODIGIOUS
Hence the rank of the word PRODIGIOUS
= 2(9!/2!x2!) + 2(9!/2!) + 2(8!/2!x2!) + 2(8!/2!) + 2(7!/2!x2!) + (7!/2!) + (5!/2!) + 2
Hint: 2 is added in the last because SU is arranged as US
= 544320+60480+5040+60+2
= 609902
2. If all the letters of the word ARUNKUMAR arranged as in a dictionary, what is the 50th word?
Solution:
Correct order of letters is A,A,K,M,N,R,R,U,U
Number of the word begins with AAKM= 5! /2!x2! = 30
Number of the word begins with AAKN = 5! /2!x2! = 30 ( exceeds rank so N fixed as 4th letter)
Number of the word begins with AAKNM = 4! / 2!x2! = 6
Number of the word begins with AAKNR = 4!/2! = 12
So the next remaining words AAKNUMRRU = 49th rank
AAKNUMRUR = 50th rank
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