Question

The freshman class has 160 students. Each freshman must write three reports from a list of 12 novels that the teacher has assigned them to read. How many different combinations of novels can a freshman student choose to write reports on? 36 220 480

Answer 1

220, because each student, can write 

12 and choose 3 possible combination of reports which is n!(n−k)!k!=220.  

Answer 2

Answer with explanation:

Number of students in freshman class = 160

Total number of novels = 12

As, each freshman must write 3 reports , means selecting 3 novels out of 12 novels.

As,selection means order of choosing novels is not important.

So, we will apply rule of combinatorics here.

Selecting 3 novels out of 12 novels , is different combinations of novels that a freshman student  can choose to write reports on is given by

    $_{3}^{12}\textrm{C}\\\\=\frac{12!}{(12-3)!3!}\\\\=\frac{12!}{9!\times3!}\\\\=\frac{12*11*10*9!}{9!*3*2*1}\\\\=11*10*2=220$

Option B:220