Multiple choice

Different words are being formed by arranging the letters of the word ARRANGE. All the words obtained are written in the form of a dictionary The rank of the word ARRANGE in a dictionary is

  1. 344

  2. 342

  3. 343

  4. 340
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find the rank of ARRANGE, we arrange its letters alphabetically: A, A, E, G, N, R, R. We then count the number of words that come before ARRANGE alphabetically. This includes words starting with AA (60), AE (60), AG (60), AN (60), ARA (24), ARE (24), ARG (24), ARN (24), ARRAE (2), ARRAG (2), and ARRANEG (1), summing to 341 words before ARRANGE, which makes its rank 342.

AI explanation

To find the dictionary rank of ARRANGE, we arrange the 7 letters (A, A, E, G, N, R, R). Words starting with A are formed by the remaining 6 letters, so we check the second letter. Starting with AAE gives 4! divided by 2! arrangements, which is 12. Starting with AAG gives 4! divided by 2!, and starting with AAN gives 4! divided by 2!, making 36 words. Next, words starting with ARAE give 3! arrangements, and ARAG gives 3! arrangements, adding 12 more words for a total of 48. Following this counting method sequentially until reaching ARRANGE yields a rank of 342.

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