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3 years ago

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The freshman class has 160 students. Each freshman must write three reports from a list of 12 novels that the teacher has assign

ed them to read. How many different combinations of novels can a freshman student choose to write reports on? 36 220 480

2 answers:

Novosadov [1.4K]3 years ago

5 0

220, because each student, can write

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

a_sh-v [17]3 years ago

3 0

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

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