Final answer:
The question involves calculating the probability of selecting 10 good bolts from a batch of 80 good and 10 broken bolts, using the combinations and probability formula without replacement.
Step-by-step explanation:
The student is asking about the probability of not drawing any broken bolts when selecting 10 bolts from a group of 80 good bolts and 10 broken bolts. To calculate this, we can use the concept of combinations and probability. The first step is to find out the total number of ways to draw 10 bolts out of 90 (which is the sum of good and broken bolts).
The total number of ways to choose 10 bolts from 90 without regard to order is given by the combination formula: C(n, k) = n! / (k! * (n - k)!), where 'n' is the total number of items, 'k' is the number of items to choose, and '!' denotes factorial. In this case, n = 90 and k = 10.
We then calculate the number of ways to choose 10 good bolts from the 80 available. Again, we use the combination formula with n = 80 and k = 10.
Finally, to find the probability, we divide the number of ways to choose 10 good bolts by the total number of ways to choose any 10 bolts. This result will be the probability that all 10 bolts selected are good and none are broken.