Question

If all the permutations of the letters in the word 'OBJECT' are arranged (and numbered serially) in alphabetical order as in a dictionary, then the ${717}^{th}$ word is

• A. TOJECB
• B. TOEJBC
• C. TOCJEB
• D. TOJCBE

Answer 1

The correct option is D TOJCBE

The order of letters of the word "OBJECT' is B C E J O T
Words starting with:
B can be formed in $5!=120$
C can be formed in $5!=120$.Total = 240
E can be formed in $5!=120$. Total = 360
J can be formed in $5!=120$. Total = 480
O can be formed in $5!=120$. Total = 600
TB can be formed in $4!=24$. Total = 624
TC can be formed in $4!=24$. Total = 648
TE can be formed in $4!=24$. Total = 672
TJ can be formed in $4!=24$. Total = 696
TO can be formed in $4!=24$. Total = 720
So, we have exceeded 717. We need to go back by 3.
Last word with TO is TOJECB ---- number 720
Before that comes TOJEBC ----- number 719
Before that comes TOJCEB ----- number 718
Before that comes TOJCBE ----- number 717
Hence, (D) is correct.