Can you help me with my finite math?

Question

There are 5 rotten apples in a crate of 25 apples.

a.) How many samples of 3 apples can be drawn from the crate?

b.) How many samples of 3 could be drawn in which all 3 are rotten?

c.) How many samples of 3 could be drawn in which there are two good apples and one rotten apple?


**Decide whether each exercise involves permutation or combinations, and then solve.***

Please try to explain how you came up with the answer and if you don't know please just leave all stupid comments to yourself.

Answer 1

All of these exercises involve combinations since the order in which you pull the apples out of the crate does not matter (at least that's how I'm interpreting the problem). The number of ways to choose r objects out of n objects is given by:
C(n,r) = n!/(r!(n-r)!). If you want to know where this equation comes from, check out the source below.
a) We're choosing 3 apples from 25 apples, so C(25,3).
b) We're choosing 3 rotten apples from the 5 total rotten apples, so C(5,3).
c) We're choosing 2 good apples from a total of 20 good apples, which can be done C(20,2) ways. Then we choose 1 rotten apple from the 5 total rotten apples, which can be done in C(5,1) ways. The total number of ways to choose 2 good and 1 rotten apples is just the product of those values, which is C(20,2)*C(5,1).
Use the above equation to find the numerical values for each C(n,r).