2012 AMC 12B Problem 16

Each song is liked by exactly one of the three pairs, by a single girl, or by no one. Every pair must be represented. Case $1:$ every song is liked by a pair. One pair gets two of the four songs ($\binom42=6$ ways, and $3$ choices for which pair), and the other two pairs get one song each ($2$ ways). This gives $3\cdot6\cdot2=36.$ Case $2:$ three songs go to the three pairs (one each) and the fourth song is liked by a single girl or no one. Assigning the four songs to these four roles gives $4!=24$ ways, and the leftover role has $4$ options (Amy, Beth, Jo, or no one): $24\cdot4=96.$ The total is $36+96=132.$ Thus, the correct answer is B.