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

Moderate

Solution

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 $\cdot$ 5! +2 $\cdot$ 4!+2 = 530

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