A teacher can make 35 quizzes.
Step-by-step explanation:
Given that,
Total problems = n = 7
Number of questions in a quiz = r = 4
We need to find the ways in which different 4-question geometry quizzes can a teacher make if there are 7 different problems to test.
For that, the combination is used: nCr = [tex]\frac{n!}{r!(n-r)!}[/tex]
By putting the values, we get
[tex]\frac{7!}{4!(7-4)!}[/tex]
[tex]\frac{7*6*5*4!}{4!*3!}[/tex]
[tex]\frac{7*6*5}{3*2*1}[/tex]
35 quizzes
Hence, a teacher can make 35 quizzes.
