How many different ways can she arrange these 5 beads on the necklace

Question

Ashley is making a bead necklace using 5 different coloured beads as shown,she decided that the red and black will stay next to each other.

Answer 1

Hi,

To solve this use permutation or counting principle. The beads are ordered in a different arrangement each time to arrive at a unique necklace.

 

You need to consider the Red and the Black as one bead, since she decided that they stay next to each other.

You also have to consider that the order of the Red and the Black :

 

1. Red-Black        ₄P₄= 24
2. Black-Red         ₄P₄= 24

There are 48 different necklaces: 24 + 24 = 48

 

I think this is helpful.

 

SN