In how many distinct arrangements of the letters of the word BANANAS are no two A's next to each other?

Answer and explanation

Correct answer: A. 120

  1. Step 1: Count letter frequencies in BANANAS: , , , (total letters).
  2. Step 2: Arrange the four consonants (B, N, N, S) first: ways.
  3. Step 3: The arranged consonants create available separated gaps (including ends): . To keep all three A's apart, choose distinct gaps out of : ways.
  4. Step 4: Multiply consonant arrangements by gap selections: .
Answer
120.
Why not the others: is the total unrestricted arrangements of the letters.

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