An inspector selects three parts (without replacement) from each batch of parts produced by a production line; the batch fails inspection if at least one of these three parts is defective. (a) Compute the probability that a batch fails inspection when it contains 25 parts, of which four are defective. (b) Compute the probability that a batch fails inspection when it contains 50 parts, of which two are defective. (c) If one batch like the one described in Part (a) is inspected each day, what is the average number of days until the first failed inspection