Question

Anna is making a bracelet and has 3 green beads, 3 blue beads, and 3 red beads available to use. The bracelet can contain at least one but at most four spherical beads of identical size on a loop of string. How many distinct bracelets could she possibly make?

a) 27
b) 54
c) 81
d) 108

Answer 1

Anna can make a total of 255 distinct bracelets using the available beads.

Step-by-step explanation:

Anna can make a bracelet with at least one but at most four spherical beads of identical size. She has 3 green beads, 3 blue beads, and 3 red beads available to use. To find the total number of distinct bracelets she can make, we need to consider all possible combinations of bead colors and bead sizes on the bracelet. We can break down the problem into four cases:

1. Case 1: Bracelet with one bead - Anna can choose any one of the 9 beads available. So, there are 9 possible bracelets in this case.
2. Case 2: Bracelet with two beads - Anna can choose any two beads from the 9 beads available. The order in which she arranges the beads does not matter. So, the number of possibilities is given by the combination formula, which is C(9, 2) = 36.
3. Case 3: Bracelet with three beads - Anna can choose any three beads from the 9 beads available. Again, the order does not matter. So, the number of possibilities is given by the combination formula, which is C(9, 3) = 84.
4. Case 4: Bracelet with four beads - Anna can choose any four beads from the 9 beads available. The order does not matter. So, the number of possibilities is given by the combination formula, which is C(9, 4) = 126.

Adding up the possibilities from all four cases, we get a total of 9 + 36 + 84 + 126 = 255 distinct bracelets that Anna can make. Therefore, none of the given options (a), b), c), d)) match the correct answer.