Question

How many different 4-question geometry quizzes can a teacher make if there are 7 different problems to test on?.

Answer 1

Answer:

35 quizzes

Step-by-step explanation:

We need to determine how many ways we can choose 4 questions out of 7 to make the quizzes.

We do this by using the formula $\displaystyle nCr=\frac{n!}{r!(n-r)!}$ which describes the number of ways we can choose $r$ objects given $n$ possible choices. So, if $n=7$ and $r=4$, then:

$_4C_7=\frac{7!}{4!(7-4)!}\\\\_4C_7=\frac{7*6*5*4!}{4!*3!}\\\\_4C_7=\frac{210}{6}\\\\_4C_7=35$

Hence, the teacher can make 35 different geometry quizzes.