Engineering Board Exam Reviewer · Permutations · hard

How many different 3-letter arrangements (not necessarily meaningful words) can be formed from the letters of the word DIAGRAM?

  1. 210
  2. 120
  3. 105
  4. 135

Answer

D. 135

Solution

The letters are D, I, A, G, R, A, M (the letter A appears twice). Case 1: no repeated A, using the 6 distinct letters: 6P3=120. Case 2: both A's used plus one of the other 5 letters, arranged in 3 ways: 5×3=15. Total =120+15=135.

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