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

There can be a maximum of 500 sets, each containing one tumbler of each color.

Step-by-step explanation:

To determine the number of sets that can be made, we need to find the minimum number of cups of each color among the three batches. Since each batch has 500 tumblers, the minimum number of cups of each color is also 500.

Therefore, there can be a maximum of 500 sets, each containing one tumbler of each color.

Answer 2

The total number of possible sets is 125,000,000.

Step-by-step explanation:

3 batches of plastic tumblers are red batch, yellow batch, and purple batch.

There are 500 tumblers in each batch.

We need to make a set 3 tumblers that contain 1 tumbler of each color.

The possible ways to select r items from total n items is

`^nC_r=(n!)/(r!(n-r)!)`

The possible ways to select 1 red tumbler from 500 tumblers red is

`^(500)C_(1)=(500!)/(1!(500-1)!)=(500* 499!)/(499!)=500`

The possible ways to select 1 yellow tumbler from 500 tumblers yellow is

`^(500)C_(1)=(500!)/(1!(500-1)!)=(500* 499!)/(499!)=500`

The possible ways to select 1 purple tumbler from 500 tumblers purple is

`^(500)C_(1)=(500!)/(1!(500-1)!)=(500* 499!)/(499!)=500`

Total possible ways to make a set of 3 tumblers that contain 1 tumbler of each color are

`500* 500* 500=125000000`

Therefore the total number of possible sets is 125,000,000.