There are 12 CD's in a bag -- 6 rap music, 3 country music, and 3 rock music. Two CD's are selected from the bag. The first CD is not replaced before making the second selection. What is the total number of possible out outcomes?

To find the total number of possible outcomes, we can use the concept of combinations.

In this case, we have a bag with 12 CDs - 6 rap music, 3 country music, and 3 rock music. We want to choose 2 CDs without replacement, which means once a CD is selected, it cannot be chosen again.

To calculate the total number of possible outcomes, we need to find the number of combinations of 2 CDs that can be formed from the 12 CDs in the bag.

The formula for combinations is:

C(n, k) = n! / (k! * (n-k)!)

where n is the total number of items and k is the number of items chosen.

In this case, n = 12 (total number of CDs) and k = 2 (number of CDs to be selected).

Substituting values into the formula:

C(12, 2) = 12! / (2! * (12-2)!)
= 12! / (2! * 10!)

Now we can calculate the values:

12! = 12 * 11 * 10! = 12 * 11!
2! = 2 * 1 = 2
(12 - 2)! = 10!

Substituting these values:

C(12, 2) = (12 * 11!) / (2 * 10!)

Now we can simplify:

C(12, 2) = 66

Therefore, the total number of possible outcomes is 66.