A dictionary is printed consisting of $$7$$ lettered words only that can be made by rearranging the letters of the word CRICKET. If the words are printed in alphabetical order, as in a standard dictionary, then the number of words before the word CRICKET is

Question

Infinity Learn · Accepted Answer

Number of words begin with CC is   $$=5$$!Number of words begin with   CE is  $$=$$ $$5$$!Number of words begin with CI is $$=$$ $$5$$!Number of words begin with CK is $$=5$$!Number of words begin with CRC is $$=4$$!Number of words begin with CRE is $$=4$$!Number of words begin with CRICE is $$=2$$!Next word is CRICKET . So number of words before the CRICKET is $$=$$ $$4$$·$$5$$! $$+2$$·$$4$$!$$+2$$ $$=$$ $$530$$

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A dictionary is printed consisting of 7 lettered words only that can be made by rearranging the letters of the word CRICKET. If the words are printed in alphabetical order, as in a standard dictionary, then the number of words before the word CRICKET is

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