"CRICKET" alphabetically: C, C, E, I, K, R, T.

Compute Permutations for Each Case:

Starting with C followed by C (CC): Calculate permutations of the remaining letters E, I, K, R, T. This would be $ 5! = 120 $ ways.

Starting with C followed by E (CE): Calculate permutations of the remaining letters C, I, K, R, T. This would also be $ 5! = 120 $ ways.

Starting with C followed by I (CI): Calculate permutations of the remaining letters C, E, K, R, T. Again, $ 5! = 120 $ ways.

Starting with C followed by K (CK): Calculate permutations of the remaining letters C, E, I, R, T. Again, $ 5! = 120 $ ways.

Starting with C followed by R and then C (CRC): Calculate permutations of the remaining letters E, I, K, T. This is $ 4! = 24 $ ways.

Starting with C followed by R and then E (CRE): Calculate permutations of the remaining letters C, I, K, T. This also results in $ 4! = 24 $ ways.

Starting with CRIC: You need to arrange the remaining letters K, E, T. "CRICE" results in 2 distinct permutations:

CRICEK

CRICKET (the word we are interested in)

Therefore, the number of arrangements before CRICKET is 2 (starting at CRICE_).

Determine the Rank:

The rank of "CRICKET" is therefore $ 120 + 120 + 120 + 120 + 24 + 24 + 2 + 1 = 531 $.

Thus, the rank of the word "CRICKET" is 531 in the list of all possible permutations arranged in dictionary order.

Permutations And Combinations

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