Find the number of ways in which 5 different beads can be arranged to form a necklace..?...

ans is 12

plzz explain how

fix  one bead..

now u have  to arrange 4 different objects..

that can be done in 4! ways..

divide it by 2 ..as half of them r similar to the other half ways..(remember it is circular )

so ur  answer is..4!/2  = 12

ENJOY

For necklaces,garlands etc,clockwise permutations=anti-clockwise.Thus,the no.of permutations become half.The no. of circular permutations of n things=(n-1)!.Thus,In this case,they become (1/2)(n-1)!.Put n=5 to get the ans.

see there are two cases in circular permutations

case1. when distinction is made between clockwise and anticlockwise permutations(as in arranging humans).

In this case we use (n-1)!

case2. when no distinction is made (like arranging flowers in garlands or beads in necklace)

Here we use (n-1)!/2