Final answer:
The problem involves combinations as the order of selection does not matter. You calculate the number of 3-apple samples from 25 using combinations, as well as specifically for 3 rotten, and mixtures of good and rotten apples.
Step-by-step explanation:
The exercise provided involves solving problems related to combinations, not permutations. Combinations are used when the order of selection does not matter. Here's how you can solve each part of the problem:
- To find how many samples of 3 apples can be drawn from a crate of 25 apples, we use the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, and k is the number of items to choose. So here, it would be C(25, 3).
- To find how many samples of 3 could be drawn in which all 3 are rotten, since there are 8 rotten apples, we calculate C(8, 3).
- To find how many samples of 3 could be drawn in which there are two good apples and one rotten apple, we calculate the combination of choosing 2 out of the 17 good apples and 1 out of the 8 rotten apples, which is C(17, 2) * C(8, 1).