How many ways can you purchase 5 cds if there are 6 to choose from, 2 cassettes if there are 5 to choose from, and 4 dvds if there are 8 to choose from?

Part of the scope of the subject area of probability is the number of arrangements of 'r' objects out of 'n' total objects. These can be classified into two types: combination and permutation. Combination is what is referred to when you arrange the objects without repetition or when order does not matter. Otherwise, it is permutation. 

In this case, this problem is a combination problem. The equation for this is:

Number of ways = n!/r!(n-r)!, where you choose 'r' things out of 'n' objects. Applying this equation, the solution would be:

5 CD's out of 6:
Number of ways = 6!/5!(6-5)! = 6 ways

2 Cassettes out of 5:
Number of ways = 5!/2!(5-2)! = 10 ways

4 DVDs out of 8
Number of ways = 8!/4!(8-4)! = 70 ways

Wow. that is a really cool question.