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CA Foundation · Quantitative Aptitude · Permutations and Combinations

A necklace is to be made by stringing 6 different coloured beads on a thread, and it can be turned over so that clockwise and anticlockwise arrangements look identical. How many distinct necklaces are possible?

The answer is 60. Six distinct beads in a circle can be arranged in 5! = 120 ways, but a necklace can be flipped over, so each arrangement and its mirror image are the same. Dividing by 2 gives 60 distinct necklaces.

  1. A120
  2. B60Correct
  3. C720
  4. D360

Explanation

Circular arrangements of 6 distinct beads = (6-1)! = 120. Since the necklace can be flipped, clockwise and anticlockwise arrangements are the same, so divide by 2: 120/2 = 60. The option 120 ignores the flipping.

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