The probability that apples will have a skin blemish A box contains $100$ apples, of which $8$ have skin blemishes. A random sample of $5$ apples is chosen. What is the probability that the sample will contain: 1. no blemishes. 2. $1$ blemish. 3. $2$ blemishes. I'm not really sure how to go about this. I think for 1. you can say $\displaystyle\frac{92\choose5}{100\choose5} \approx 0.6531909671$ but I'm not sure. I just chose $5$ from the $92$ apples that do not have blemishes over the total. The other questions I don't know.

Your answer for problem 1 looks good. And the idea you used can be applied to the other two problems:

For instance for 2., you would choose 1 blemished apple ( $\left( \begin{array}{c} 8\\\1 \end{array}\right)$ possible ways), and 4 unblemished apples ($\left( \begin{array}{c} 92\\\4 \end{array}\right)$ possible ways).

So the probability of 1 blemished apple (and 4 unblemished) is $$\frac{ \left( \begin{array}{c} 8\\\1 \end{array}\right)\left( \begin{array}{c} 92\\\4 \end{array}\right) }{\left( \begin{array}{c} 100\\\5 \end{array}\right) }$$