Multiple choice

The total number of ways, in which letters of the word 'ACCOST' can be arranged, so that the two C's never come together, is

  1. 120

  2. 180

  3. 240

  4. 360

  5. 720
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total letters = 6 (A, C, C, O, S, T). Total permutations = 6! / 2! = 360. Arrangements where C's are together: Treat CC as one unit. Total units = 5. Permutations = 5! = 120. Arrangements where C's are not together = 360 - 120 = 240.

AI explanation

The word ACCOST has 6 letters with the letter C repeated twice, so the total arrangements are 6 factorial divided by 2 factorial, which is 360. To find arrangements where the two C's are together, treat the two C's as a single unit, making 5 units in total. These 5 units can be arranged in 5 factorial ways, which is 120. Subtracting the arrangements where C's are together from the total gives 360 minus 120, which equals 240.

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