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nCr Definitions and Properties

A dictionary ...

Question

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

A

530

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B

480

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C

531

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D

481

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Solution

The correct option is A 530
The number of words before the word CRICKET is $4 \times 5! + 2 \times 4! + 2! = 530$

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