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Question
If the letters of the word RACHIT are arranged in all possible ways as listed in dictionary. Then what is the rank of the word RACHIT?
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Solution
The alphabetical order of RACHIT is A, C, H, I, R and T
Number of words beginning with A = 5!
Number of words beginning with C = 5!
Number of words beginning with H = 5!
Number of words beginning with I = 5!
And Number of word beginning with R i.e. RACHIT = 1
∴ The rank of the word ‘RACHIT’ in the dictionary
= 5! + 5! + 5! + 5! + 1
= 4 × 5! + 1
= 4 × 5 × 4 × 3 × 2 × 1 + 1
= 4 x 120 + 1
= 480 + 1
= 481
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