Permutations And Combinations Question 8

Question: The number of ways in which 5 beads of different colours form a necklace is [RPET 2002]

Options:

A) 12

B) 24

C) 120

D) 60

Show Answer

Answer:

Correct Answer: A

Solution:

  • The number of ways in which 5 beads of different colours can be arranged in a circle to form a necklace are $ (5-1)\ !=4\ ! $ . But the clockwise and anticlockwise arrangement are not different (because when the necklace is turned over one gives rise to another) Hence the total number of ways of arranging the beads $ =\frac{1}{2}(4\ !)=12 $ .



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