First slide

Permutations

Question

The number of ways in which you can put five beads of five different colours to form a necklace is:

Moderate

A

12
B

24
C

60
D

120

Solution

Number of ways of putting beads in a necklace is 4! But clockwise arrangement abcde and anticlockwise arrangement aedcb are not really different, for, the arrangement abcde gives rise to arrangement aedcb if the necklace is turned over.
$∴$ required number of ways $= \frac{1}{2} (4!) = 12$

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