Question

You've just finished making 3 batches of plastic tumblers: a red batch, a yellow batch, and a purple batch. There are 500 tumblers in each batch. You are now making sets of 3 tumblers that contain 1 tumbler of each color. How many sets can you make?

Answer 1

Answer: Since there are 500 tumblers in each batch, there are a total of:

500 tumblers/batch × 3 batches = 1500 tumblers

To make a set of 3 tumblers with one tumbler of each color, we can choose one tumbler from each batch. There are 500 choices for the tumbler from the red batch, 500 choices for the tumbler from the yellow batch, and 500 choices for the tumbler from the purple batch. Therefore, there are:

500 choices for the first tumbler × 500 choices for the second tumbler × 500 choices for the third tumbler = 500^3 = 125,000,000 possible sets of 3 tumblers.

However, we are interested in the number of sets that can be made from the available tumblers. Each set requires one tumbler from each batch, and since there are 500 tumblers in each batch, we can make:

500 sets/batch = 500 sets/batch × 3 batches = 1500 sets

Therefore, we can make a total of 1500 sets of 3 tumblers from the available tumblers.

Explanation: