Competition problem — Combinatorics

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Combinatorics Difficulty 2.9 Junior Find the answer

A factory produces three different models of products: A, B, and C, with production quantities of 400, 800, and 600 units, respectively. To inspect the products' quality, 90 units are randomly selected using stratified sampling from all products for inspection. The number of units to be selected from model C is _______.

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

From the given information, we should select from model C:

$\frac{90}{400 + 800 + 600} \times 600 = 30 \text{ units}.$

So the answer is $\boxed{30}$ .

This is because stratified sampling uses random sampling, meaning that the sampling ratio is equal for all strata. The sampling ratio is:

$\frac{90}{400 + 800 + 600} = \frac{1}{20}.$

Thus, the number of units to be selected from model C is $600 \times \frac{1}{20} = 30 \text{ units}$ .

This problem tests the understanding of stratified sampling and basic analytical skills, making it a fundamental question.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.