6. A shipment of 250 netbooks contains 3 defective units. Determine how many ways a vending company can buy three of these units and receive
c. at least one good unit.

검증된 단계별 안내

Step 1: Understand the problem. We are tasked with finding the number of ways to select 3 units from a shipment of 250 netbooks, where at least one of the selected units is not defective. This means we need to exclude the cases where all 3 selected units are defective.

Step 2: Calculate the total number of ways to select 3 units from the shipment. Use the combination formula: C(n, r) = n! / (r!(n - r)!), where n is the total number of items (250) and r is the number of items to choose (3). This gives us C(250, 3).

Step 3: Calculate the number of ways to select 3 defective units. Since there are only 3 defective units in the shipment, the number of ways to select all 3 defective units is C(3, 3).

Step 4: Subtract the number of ways to select all defective units from the total number of ways to select 3 units. This ensures that at least one of the selected units is not defective. The formula is: Total ways - Ways to select all defective units = C(250, 3) - C(3, 3).

Step 5: Simplify the expressions for C(250, 3) and C(3, 3) using the combination formula, but do not compute the final values. This will give you the number of ways to select 3 units with at least one good unit.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Combinatorics

Combinatorics is a branch of mathematics dealing with combinations and permutations of objects. In this context, it helps determine the number of ways to select units from a larger set, which is essential for calculating the different combinations of defective and non-defective netbooks.

Complementary Counting

Complementary counting is a technique used to simplify counting problems by calculating the total number of outcomes and subtracting the number of undesired outcomes. Here, it can be applied to find the number of ways to select three units that include at least one good unit by first calculating the total combinations and then subtracting the combinations that consist only of defective units.

Probability

Probability is the measure of the likelihood that an event will occur, often expressed as a fraction or percentage. In this scenario, understanding the probability of selecting at least one good unit from the shipment is crucial for evaluating the effectiveness of the vending company's purchase strategy.

6. A shipment of 250 netbooks contains 3 defective units. Determine how many ways a vending company can buy three of these units and receivec. at least one good unit.