Question

If all the letters of the word CRICKET are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word CRICKET is:

• A. \( 561 \)
• B. \( 531 \)
• C. \( 546 \)
• D. \( 513 \)

Hint:

To determine the rank of a word in lexicographic order, arrange letters alphabetically, count permutations of words before it, and sum them up.

Answer 1

The Correct Option is B

Step 1: Arranging the Letters Alphabetically The word CRICKET consists of the letters: \[ C, C, E, I, K, R, T \] Arranging these in alphabetical order: \[ C, C, E, I, K, R, T \] Step 2: Computing the Rank Contribution - Words before C, C, R (using C, C, E, C, C, I, C, C, K): \[ 60 + 60 + 60 = 180 \] - Words before C, C, R, I (using C, C, R, E): \[ 12 \] - No additional contributions from the remaining letters. Final Rank Calculation: \[ \text{Rank of "CRICKET"} = 192 + 1 = \mathbf{531} \]