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

Answer: (D)

The order of letters of the word 'OBJECT' is B CE J T
Words starting with $B$ can be formed in $5!$ ways.
Words starting with $C$ can be formed in $5!$ ways.
Words starting with $E$ can be formed in $5!$ ways.
Words starting with $J$ can be formed in $5!$ ways.
Words starting with $O$ can be formed in $5!$ ways.
Words starting with TB can be formed in $4!$ ways.
Words starting with TC can be formed in $4!$ ways.
Words starting with TE can be formed in $4!$ ways.
Words starting with TJ can be formed in $4!$ ways.
Words starting with TOB can be formed in $3!$ ways.
Words starting with TOC can be formed in $3!$ ways.
Words starting with TOE can be formed in $3!$ ways.
Words starting with TOJB can be formed in $2!$ ways.
Words starting with TOJC can be formed in $2!$ ways.
Therefore, the total number of words is 718 words.
Hence, 717 th word is TOJCBE.