GRE quant question (hard)?

Question

"I got this question from the GRE book. Central state college has three sections of Math 102. If four students, Bill, Jill, Phill, and Will decide to transfer from Math 101 into Math 102, in how many ways can the four students be assigned to the three sections, if each section must receive at least on new student? A)12 B)18 C)24 D)27 E)36 I don't know how to solve this question, and I don't have a solution. Could you help me do this? Thank you in advance. "

Answer 1

We assign four students to 3 sections so that at least one student is in each section. Therefore, two students are placed into one of the sections and one student is placed into each of the other two sections. In other words, we distribute a set of 3 different objects (for example, one pair BJ and two single students P and W) putting 1 object into each one of 3 sections. We know that number of permutations for 3 objects is 3! = 3*2*1 = 6. Choosing a different pair of students from 4 students we have 4!/[2!(4 - 2)!] = 6 different sets, namely, {BJ, BP, BW, JP, JW and PW}. Again, each set has 6 permutations, and thus 6 different sets can be assigned in 6x6 = 36 ways.