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  4. 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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Q. 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

Permutations and Combinations

Solution:

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.