Jeanine is selecting various albums to be displayed in the front of her music coffee house. She will be choosing 4 albums for one part of the display. This part of the display is very prominent and she is really trying to promote jazz. There are five albums from Diana Kroll, seven albums from Harry Connick Jr. and four albums from Michael Bublé. In how many ways can she choose four albums for display and at least two albums are from Diana Kroll? Evaluate using both the direct and indirect method.
+130515 I get something a little different here....at least two DK albums means we want to choose either 2, 3 or 4 of Diana Kroll's albums.
Choosing 2 we have C(5,2)*C(11,2) = 550 ways
Choosing 3 we have C(5,3)*C(11,1) = 110 ways
Choosing 4 we have C(5,4)*C(11,0) = 5 ways
So 550 + 110 + 5 = 665 ways
And that's the direct method
For the indirect method, we want to take all the possible ways of choosing 4 albums and subtract the ways that don't include choosing just one or none of the DK albums...so we have....
C(16,4) - C(5,1)*C(11,3) - C(5,0)*C(11,4) = 665 ways
+130515 I get something a little different here....at least two DK albums means we want to choose either 2, 3 or 4 of Diana Kroll's albums.
Choosing 2 we have C(5,2)*C(11,2) = 550 ways
Choosing 3 we have C(5,3)*C(11,1) = 110 ways
Choosing 4 we have C(5,4)*C(11,0) = 5 ways
So 550 + 110 + 5 = 665 ways
And that's the direct method
For the indirect method, we want to take all the possible ways of choosing 4 albums and subtract the ways that don't include choosing just one or none of the DK albums...so we have....
C(16,4) - C(5,1)*C(11,3) - C(5,0)*C(11,4) = 665 ways
