Math Problem Statement
A factory received a shipment of 49 generators, and the vendor who sold the items knows there are 6 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators 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 6 generators is selected, find the probability that all in the sample are defective.
If a sample of 6 generators is selected, find the probability that none in the sample are defective.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Combinatorics
Formulas
Combination formula: C(n, k) = n! / (k!(n-k)!)
Probability formula: P(A) = favorable outcomes / total outcomes
Theorems
Combination theory
Basic probability principles
Suitable Grade Level
Grades 10-12
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