Wednesday, March 7, 2007

Wednesday, March 7

Today's class we were broken into groups and told to solve a couple of problems. The first problem was this...

1. An examination consists of 13 questions. A student must answer one of the first two questions and only nine of the remaining ones. How many choices of questions does the student have?

Many of us had different answer but all were wrong lol but they were all right in their own way.
Had the question been a pick question the answer 1+11! would of been close to being right. If it asked for probability the answer of 1/2 x 9/11 = 9/22 would of been on the right track. Now 13 was right in the sense that yes they are 13 questions to choose from.

Now because the question asks how many choices does the student have? The formula that should be used to answer this question would be the choose formula.

~Your first step would be to punch in 2 nCr 1 into your calculator. This is because in part A the student has to answer one out of two questions. The answer you should get is 2.

~Your second step would to punch in 11 nCr 9 into your calculator. Because in part B you have 11 possible questions left that can be answer but you only have to answer nine of them. The answer you should get is 55.

~ Finally you take 2 x 55 which will give you 110 as your finally answer.

Things to remember.

1. Factorial notation (!) is used when using the pick formula. Ex. How many books can be arranged on a book shelf? So you would go 12! to get your answer.

2. On any tests or the exam if you are given a choose question, and you write your answer for example as 11 nCr 9 it will be marked WRONG your answers should be written as 11 C 9

The next question we were given was...

Randomly arranged on a bookshelf are five thick books, 4 medium sized books and, 3 thin books. What is the probability that the books of the same size stay together?

The way we did this in class was we broke the questions into 3 parts.

1. How many ways can the 12 books be rearranged on the bookshelf?

while because we don't care what order they are in all you need to do is go 12!.

so 12! gives you 479 001 600.

2. How many ways will the books of the same size stay together.

There are 3 sizes of books, so say you put each book of the same size into a different bag. Now you only have 3 object to rearrange. With this your answer is 3! but now if you open bag one just rearrange the books by themselves you get 5! because there are 5 thick books. Bag two would give you 4! because there are four medium-sized books and bag three would be 3! because there are three thin books.

so with this you take 3! x 5! x 4! x 3! = 103 680

3. What is the probability of the books of the same size stay together?

You already have your fraction so the question is pretty much done, you take

(3! x 5! x 4! x 3!) / 12!

Sorry for the way the fractions are written i couldn't figure out how to do the normal line.

The next scribe is Tennyson

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