Question

Joanna has six beads that she wants to assemble into a bracelet. Two of the beads have the same color, and the other four all have different colors. How many different ways can Joanna assemble her bracelet

Answer 1

Joanna can assemble her bracelet in 30 ways.

How to find the number of ways in which the bracelet can be assembled?

It is given that Joanna has 6 beads and of those 6 beads, 2 are of the same color.

The rest 4 are of different colors.

Six beads can be arranged in a circle in 6!/6 ways.

This means that the six beads can be arranged in 5! ways.

Since this is a bracelet, it can be flipped around. Therefore, it can be arranged in 5!/2 ways.

5!/2 = 5*4*3*2*1/2

= 60

Now, we know that two beads are of the same color. Therefore, we must divide this by two again.

Therefore, we get:

60/2 = 30

The six beads can be arranged in 30 ways to make the bracelet.

Therefore, we have found that Joanna can assemble her bracelet in 30 ways.

Learn more about permutations here: https://brainly.com/question/1216161

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