A student wants to buy 3 CDs, but assume that there are 3 CDs featuring the piano, 5 CDs featuring the trumpet, and 3 CDs featuring the saxophone. In how many ways can the selection be made if CD's featuring at least 2 different instruments are selected?

Answer 1

So we can't have
TTT
PPP
SSS

could have
PST --- C(3,1) x C(3,1) x C(5,1) = 4
PPT --- C(3,2) x C(5,1) = 15
PPS --- C(3,2) x C(3,1) = 9
TTP --- C(5,2) x C(3,1) = 30
TTS --- C(5,2) x C(3,1) = 30
SSP --- C(3,2) x C(3,1) = 9
SST --- C(3,2) x C(5,1) = 15

total = 108

Answer 2

108 is not correct. Thanks for trying tho Reiny!

Answer 3

It was a simple typo,
in the first of the listings , it should have been

PST --- C(3,1) x C(3,1) x C(5,1) = 45
changing my total to 153