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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

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TOJECB

TOCJEB

TOJEBC

TOJCBE

answer is D.

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Detailed Solution

The alphabetical order of letters of the word $‘ O B J E C T ’$ is $B C E J O T$

Word starting with can $B$ be formed in $5!$ ways

Word starting with can $C$ be formed in $5!$ ways

Word starting with can $E$ be formed in $5!$ ways

Word starting with can $J$ be formed in $5!$ ways

Word starting with can $O$ be formed in $5!$ ways

Word starting with can $T B$ be formed in $4!$ ways

Word starting with can $T C$ be formed in $4!$ ways

Word starting with can $T E$ be formed in $4!$ ways

Word starting with can $T J$ be formed in $4!$ ways

Word starting with can $T O B$ be formed in $3!$ ways

Word starting with can $T O C$ be formed in $3!$ ways

Word starting with can $T O E$ be formed in $3!$ ways

Word starting with can $T O J B$ be formed in $2!$ ways

Word starting with can $T O J C$ be formed in $2!$ ways

There fore, the total number of words is $718$ Hence, $717^{t h}$ word is $T O J C B E$

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