Mathematics: 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?

You’ve just finished making 3 batches of plastic

smhrosepetals

11.03.2022

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

$^nC_r=\frac{n!}{r!(n-r)!}$

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

$^{500}C_{1}=\frac{500!}{1!(500-1)!}=\frac{500\times 499!}{499!}=500$

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

$^{500}C_{1}=\frac{500!}{1!(500-1)!}=\frac{500\times 499!}{499!}=500$

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

$^{500}C_{1}=\frac{500!}{1!(500-1)!}=\frac{500\times 499!}{499!}=500$

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

$500\times 500\times 500=125000000$

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

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