Multiple choice

Using the letters A, C, E, R, R and T, how many distinct 6‑letter strings can be formed if the two Rs are not next to each other?

  1. 120

  2. 180

  3. 210

  4. 240

  5. 300
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D Correct answer
Explanation

Total arrangements of A, C, E, R, R, T is 6!/2! = 360. Arrangements where Rs are together (treat RR as one unit) is 5! = 120. Rs not together = 360 - 120 = 240.

AI explanation

The total arrangements of 6 letters with R repeated twice is 6! / 2! = 360. Treating the two Rs as a single unit makes 5 distinct items, which arrange in 5! = 120 ways. Subtracting the adjacent arrangements gives 360 - 120 = 240 distinct strings.

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