Question

A bracelet contains at least one but at most four spherical beads. How many different ways can the bracelet be arranged with different bead colors?

A) 4
B) 5
C) 6
D) 7

Answer 1

There are 65 different ways to arrange the bracelet with different bead colors.

Step-by-step explanation:

There are four possible scenarios for the number of beads in the bracelet: 1 bead, 2 beads, 3 beads, or 4 beads. For each scenario, we need to determine the number of ways to arrange the different bead colors.

Scenario 1: 1 bead

In this scenario, there is only one bead, so there is only one way to arrange the bead colors.

Scenario 2: 2 beads

In this scenario, there are two possibilities:

• Both beads are the same color, leading to 4 options (blue, red, green, or yellow).
• The beads are different colors, leading to 12 options (6 choices for the first bead and 2 choices for the second bead).

Scenario 3: 3 beads

In this scenario, there are 24 options (4 choices for the first bead, 3 choices for the second bead, and 2 choices for the third bead).

Scenario 4: 4 beads

In this scenario, there are 24 options (4 choices for each of the four beads).

Therefore, the total number of different ways to arrange the bracelet with different bead colors is 1 + 4 + 12 + 24 + 24 = 65.