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CA Foundation · Quantitative Aptitude · Permutations and Combinations

A necklace is to be made using 8 different beads. In how many distinct ways can the necklace be made, given that it can be turned over so clockwise and anticlockwise arrangements look the same?

The necklace can be made in 2520 ways. Circular arrangements of 8 distinct beads number 7! = 5040, but since the necklace can be flipped, each pattern is counted twice. Dividing by 2 gives 2520. Using 5040 ignores the flip symmetry.

  1. A5040
  2. B40320
  3. C2520Correct
  4. D1260

Explanation

For a necklace, clockwise and anticlockwise arrangements are identical, so the count is (n-1)!/2. With n = 8, (7!)/2 = 5040/2 = 2520. The value 5040 ignores the flipping of the necklace.

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