A shipment of 10 television sets includes three that are defective. In how many ways can a hotel

step 1 In this problem, we are given that the probability of getting a defective TV is 3 over 10 which

A shipment of 10 television sets includes three that are...

Key Concepts

At Least Condition

The 'at least' condition requires that the selection must satisfy a minimum threshold, meaning that all cases meeting or exceeding that threshold must be considered. In problems like this, it is necessary to count each scenario that satisfies the condition and then combine the results using addition.

Multiplication Principle

The multiplication principle states that if one event can occur in m ways and a second independent event can occur in n ways, then the two events together can occur in m times n ways. In selection problems with groups, such as choosing from defective and non-defective sets, it helps to calculate the number of outcomes in each category by multiplying the number of choices in each group.

Combinations

Combinations refer to the method of selecting items from a larger set such that the order of selection does not matter. This is typically expressed mathematically using the binomial coefficient, often written as n choose k, which calculates the number of ways to choose k items from n without considering the order.

Case Analysis

Case analysis involves breaking a problem into distinct cases based on different conditions—in this instance, examining separate cases based on how many defective items (either exactly 2 or exactly 3) are included in the selection. Each valid case is computed individually and then summed to obtain the final count.

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