Question:

<p><strong>Step 1:</strong> Letters in OBJECT in alphabetical order: B, C, E, J, O, T (6 letters, all distinct)</p><p><strong>Step 2:</strong> Count permutations starting with each letter (remaining 5! = 120 each):</p><ul><li>Starting with B: positions 1-120</li><li>Starting with C: positions 121-240</li><li>Starting with E: positions 241-360</li><li>Starting with J: positions 361-480</li><li>Starting with O: positions 481-600</li><li>Starting with T: positions 601-720</li></ul><p><strong>Step 3:</strong> 717th word starts with T (since 601 ≤ 717 ≤ 720). Remaining count: 717 - 600 = 117</p><p><strong>Step 4:</strong> Fix T, remaining letters: B, C, E, J, O (4! = 24 each position):</p><ul><li>TB___: positions 1-24</li><li>TC___: positions 25-48</li><li>TE___: positions 49-72</li><li>TJ___: positions 73-96</li><li>TO___: positions 97-120</li></ul><p>117 falls in TO___ range. Position within this: 117 - 96 = 21</p><p><strong>Step 5:</strong> Fix TO, remaining letters: B, C, E, J (3! = 6 each):</p><ul><li>TOB__: positions 1-6</li><li>TOC__: positions 7-12</li><li>TOE__: positions 13-18</li><li>TOJ__: positions 19-24</li></ul><p>21 falls in TOJ__ range. Position within: 21 - 18 = 3</p><p><strong>Step 6:</strong> Fix TOJ, remaining letters: B, C, E (2! = 2 each):</p><ul><li>TOJB_: positions 1-2</li><li>TOJC_: positions 3-4</li></ul><p>3 falls in TOJC_ range. Position within: 3 - 2 = 1</p><p><strong>Step 7:</strong> Fix TOJC, remaining letters: B, E (1! = 1 each):</p><ul><li>TOJCB: position 1</li><li>TOJCE: position 2</li></ul><p>1st position gives TOJCBE</p><p>∴ Answer: <strong>TOJCBE</strong></p>