Multiple choice

The number of arrangements that can be made out of the letters of the word $SUCCESS$ so that all $S$ do not come together is

  1. $60$
  2. $120$
  3. $360$
  4. $420$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total arrangements of SUCCESS (7 letters: S=3, C=2, U=1, E=1) is 7! / (3! * 2!) = 420. Arrangements where all S are together (treat SSS as one unit) is 5! / 2! = 60. Subtracting these gives 420 - 60 = 360.

AI explanation

The word SUCCESS has 7 letters with S repeated 3 times and C repeated 2 times, so the total arrangements are 7! / (3! 2!) = 420. To find the arrangements where all S do not come together, treat the three S letters as a single unit, which gives 5! / 2! = 60 arrangements. Subtracting the arrangements where all S are together from the total gives 420 - 60 = 360.

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