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?

Answer 1

the 160 part has nothing to do with the problem, so don't let it confuse you

Answer 2

the question is this : " how may ways can 3 books be chosen out of a total of 12" or in plain math "how many ways can you choose 3 out of a set of 12"
or even more briefly
"what is 12 choose 3?" sometimes written as \(_{12}C_3\) or \(\binom{12}{3}\)

Answer 3

do you know how to compute it?

Answer 4

no never taught that

Answer 5

really? then how are you expected to do it?

Answer 6

I don't know

Answer 7

i work off a computer

Answer 8

\[_{12}C_3\]
make a fraction in the top put multiply 3 numbers starting with 12 and decreasing by 1 each time, so the numerator is \(12\times 11\times 10\)

Answer 9

then the denominator do the same thing, but this time starting at 3, so the denominator is \(3\times 2\times 1\)

Answer 10

so
\[_{12}C_3=\frac{12\times 11\times 10}{3\times 2\times 1}\]
you don't need to write the 1 in the denominator

Answer 11

cancel first, multiply last
get
\[_{12}C_3=\frac{12\times 11\times 10}{3\times 2\times 1}=2\times 11\times 10=220\]

Answer 12

ok