A shipment of 120 fasteners that contains 4 defective fasteners was sent to a manufacturing plant. The

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A shipment of 120 fasteners that contains 4 defective fasteners was sent to a manufacturing plant. The plant’s quality-control manager randomly selects and inspects 5 fasteners. What is the probability that exactly 1 of the inspected fasteners is defective?

Approach Find the probability that exactly 1 fastener is defective by calculating the number of ways of selecting exactly 1 defective fastener in 5 fasteners and dividing this result by the number of ways of selecting 5 fasteners from 120 fasteners. To choose exactly 1 defective in the 5 requires choosing 1 defective from the 4 defectives and 4 non-defectives from the 116 non-defectives. The order in which the fasteners are selected does not matter, so we use combinations.

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