chantel has 10 different CD's. In how many different orders could she place them if she:

selects 5, but her only amy winehouse cd must be first and only alicia keys cd second

The first two choices are prescribed. There are 8 options for the third choice, 7 for the fourth and 6 for the fifth. That makes 8x7x6 = __ possibilities.

THX

To solve this problem, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we want to find the number of different orders in which Chantel can arrange her CDs, given the specified conditions.

Since Chantel must have the Amy Winehouse CD as the first one and the Alicia Keys CD as the second one, we can treat these two CDs as a single unit. So, we have 8 remaining CDs (10 CDs - 1 Amy Winehouse CD - 1 Alicia Keys CD = 8 CDs) to arrange along with this unit.

To find the number of different arrangements, we calculate the permutations of these 8 CDs. The formula to find permutations is n!, where n represents the number of objects to arrange.

In this case, since Chantel needs to select 5 CDs out of the 8 remaining CDs, we use the formula for permutations of selecting r objects from n objects, denoted as nPr. The formula for nPr is:

nPr = n! / (n - r)!

In this case, n = 8 (remaining CDs) and r = 5 (selected CDs). Plugging in these values, we have:

nPr = 8! / (8 - 5)!

Calculating the value of this expression, we can find the number of different orders Chantel can arrange her CDs.