The number of ways that 8 beads of different colours can be strung to form a necklace is

Step-by-step solution

The number of ways to arrange n distinct objects in a circle is (n-1)! . For a necklace, clockwise and counter-clockwise arrangements are considered identical because it can be flipped over. Therefore, the number of ways to string n different beads into a necklace is (n-1)! 2 . Given n = 8 , the number of ways is (8-1)! 2 = 7! 2 . Since 7! = 5040 , the number of ways is 5040 2 = 2520 . Answer: 2520