Professor Oger must choose between an extra writing assignmentand an extra reading assignment for the upcoming spring break. Forthe writing assignment, there are tw...

For a college application, Macawi must select one of five topics on which to write a short essay. She must also select a different topic from the list for a longer essay. How many ways can she choose the topics for the two essays?

Student must handle three out of five questions on any state test. How many possible choices are they? So they are five questions and students can take three questions. So how many possible combinations from five can she make or your Shinnick? So this order is lot off essence, so we'll use that. So this scene is equal to science. Pictorial divided by Thanks, man. Last three Victoria, which is to Victoria Times. Leave it, Claudia. So this is Oh, Victoria. Ah, let's consult the computer here. He's kind of trendy. Defined it fine. Three. Victoria times two. We're just 12 so they are attained such choices. It's a combination. What this to do could make.

A teacher is making a five question quiz but wants to make this question is different for each student so each student might receive a different quiz. For instance, there are eight questions that might pop up for number one on each test. Nine questions that might pop number 27 for number 38 for number four and six for number five. What we want to figure out is how many possible combinations of questions there are or how many possible quizzes are out there to start? We note that if this were to question quiz, numbers one and two, we would have a number of possible quizzes given simply by multiplying the options we have for each question eight times nine is equal to 72 possible quizzes. So since we're just multiply across, we see that we're using the base accounting rule, which is also known as the multiplication rule. To use the multiplication rule, all we have to do to obtain them total number of nominations is multiply the number of options per question, highlighted here, multiplying across eight times nine from seven times eight times six gives us our final answer of 24,192 possible versions of this quiz.

Callow must write on any three off the eight is the questions on the final exam in history. How many ways are there for you to pick the questions? Saw the Ah eight questions and she can choose. Hey, so we're using a combination because the question surrounding is not important. So eight Victoria off five. Victoria and Victoria that's out. Drinks find 83 and bad will give us 56 56 ways off file, aging them.

He'll unstuck, Took and select. Got two books. Art off 17 books. We had to find the total number of ways or combinations, which he can select. Two books. Art off 17 books by using combination Rule and C are equal toe and factorial. Do it in by end minus R. Factorial in tow. R factorial Pure order is not important, however. He can select those two books part off 17 books, so and factorial is 17. Factorial the order but N minus R is 17 minus two factorial into our factory. Our is toe, so to Factory 17 factorial we can write it as 17 into 16 in tow. 15 factorial do it by 17. Minus two is 15 to When we write like this, it's easy to simplify the prediction into two factory we can can sell for 15 factorial in numerator and denominator 17 in tow. 16. Divided by two factorial that is two into one. So 17 into eight is 1 36 He'll an instructor. Consulate 1 36 combination of books which he can select from 17 books toe to books