A factory received a shipment of 35 bolts, and the vendor who sold the items knows there are 8 bolts in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the bolts in the sample are defective, he will refuse the shipment. For each of the following, give your responses as reduced fractions. If a sample of 8 bolts is selected, find the probability that all in the sample are defective. If a sample of 8 bolts is selected, find the probability that none in the sample are defective.

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