In Today's Class:Why they never should have called this a combination lock.

royal combination by flickr user Darwin Bell

Permutations of non-distinguishable objects ...

Find the number of different "words" that can be made by rearranging the letters in the word:

Examples:

(a) BOOK (b) MISSISSIPPI

The number of ways to arrange n objects that contain k , k , k , ... sets of non-distinguishable objects is given by:

321

If a fair coin is tossed 4 times, what is the probability of obtaining exactly 2 heads?

If a fair coin is tossed 4 times, what is the probability of obtaining exactly 2 heads?

If a fair coin is tossed 4 times, what is the probability of obtaining exactly 2 heads?

All the letters of the word MANITOBA are arranged at random in a row. How many ways can this be done?

What is the probability that this random arrangement will have the two A’s next to each other?

How many arrangements will have the two A’s next to each other?

HOMEWORK

(a) In how many ways can the letters of the word GEOMETRY be arranged so that vowels and consonants alternate?

(b) In how many of these ways is Y the last letter?

(c) If one of these "words" is randomly selected, what is the probability that Y is the last letter?

HOMEWORK

Suppose that, when you go home from school, you like to take as great a variety of routes as possible, and that you are equally likely to take any possible route. You will walk only east or south.

How many ways can you go from the school to home?

What is the probability that you will walk past the post office on your way home?

Suppose that, when you go home from school, you like to take as great a variety of routes as possible, and that you are equally likely to take any possible route. You will walk only east or south.

How many ways can you go from the school to home?

What is the probability that you will walk past the post office on your way home?

Suppose that, when you go home from school, you like to take as great a variety of routes as possible, and that you are equally likely to take any possible route. You will walk only east or south.

How many ways can you go from the school to home?

What is the probability that you will walk past the post office on your way home?

Design an experiment using coins to simulate a 10 question true/false test. What is the experimental probability of scoring exactly 70% on the test if you guess each answer?

Solve for the exact theoretical probability of getting "at least 7" out of ten on this test.

HOMEWORK

Design an experiment using coins to simulate a 10 question true/false test. What is the experimental probability of scoring exactly 70% on the test if you guess each answer?

Let's think about this using what we've just learned ...Solve for the exact theoretical probability of getting "exactly 7" out of ten on this test.

HOMEWORK

Design an experiment using coins to simulate a 10 question true/false test. What is the experimental probability of scoring exactly 70% on the test if you guess each answer?

Let's think about this using what we've just learned ...Solve for the exact theoretical probability of getting "at least 7" out of ten on this test.

HOMEWORK