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When customers buy a product at a supermarket, there is a concern about the item being underweight. Suppose there are 20 "16-oz" ribeye steak on display and 3 of them are underweight. A customer buys 5 of 20 steaks at random. What is the probability that none of them is underweight?

My attempt was simply $\frac{17C5}{20C5}$ why is this wrong?

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  • $\begingroup$ You can also reason this scenario without "Choose". Picture Mister X grabbing the first steak. It is a random experiment. What is the probability of success? write it down. Then (assuming a store employee does not replace the grabbed steak) Mister X goes to grab his next one, and so on. $\endgroup$
    – 311411
    Mar 25, 2021 at 0:49

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Possibly it is right. 20C5 expresses the number of possible size-5 samples out of 20 steaks. Then 17C5 gives the number of possible size-5 samples from the good ones.

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