Question

Kacey is picking out jewelry to wear for school. She has 10 rings, 4 bracelets, and 4 necklaces. How many jewelry combinations are possible if she is going to wear 1 ring, 1 bracelet, and 2 necklaces?

a) 80 combinations
b) 160 combinations
c) 240 combinations
d) 320 combinations

Answer 1

Kacey can create 240 different jewelry combinations.

Step-by-step explanation:

The number of jewelry combinations possible for Kacey is determined by multiplying the number of options for each type of jewelry she can wear. According to the question, she can choose 1 ring out of 10 options, 1 bracelet out of 4 options, and 2 necklaces out of 4 options.

Therefore, the number of combinations is calculated as:

1. The number of ring options (10) multiplied by the number of bracelet options (4) multiplied by the number of necklace options (4) multiplied by the number of remaining necklace options (3), since Kacey needs to choose 2 necklaces. This results in: 10 x 4 x 4 x 3 = 480 combinations.
2. However, we need to divide this by the number of ways we can arrange the 2 chosen necklaces, which is 2! (or 2 factorial) which equals 2. This is because the order in which the necklaces are worn doesn't matter. Therefore, the final number of jewelry combinations possible for Kacey is 480 ÷ 2 = 240 combinations.