You are doing a math quiz and need to complete at least 12 geometry problems and algebra problems within 2 hours. It will take you 15 minutes to complete a geometry problem and 5 minutes to complete an algebra problem. Write a system of inequalities to express this situation. What is the most possible number of geometry problems you can complete and still meet the requirements?

there is only one way to arrange all the eight relative to each other because they are not distinct. we have

now there are nine places to place an (and not more than one in one place).   because we have four symbols, we need to choose four of these nine places to insert an . order does not matter because the are not distinct.

thus there are 1 · c(9,4) ways, or, if we calculate it,

thus there are 126 ways to form such "words."

answer: correct choices are 1, 3 and 5

step-by-step explanation: