Bento Box by flickr user Route79

How Many Different Meals?A.K.A.

The Fundamental Principle of Counting

How many ways can the word "MATHEMATICS" appear in the following array if you must spell the word in proper order? HOMEWORK

The diagram below shows a game of chance where a ball is dropped as indicated, and eventually comes to rest in one of the four locations labelled A, B, C, or D. The ball is equally likely to go left or right each time it strikes a triangle. We want to determine the theoretical probability of a ball landing in any one of these four locations. To do this, we need to know the total number of paths the ball can take, and also the number of paths to each location. HOMEWORK

Find the theoretical probability of flipping three pennies and getting at least 1 heads. HOMEWORK

"How many meals?"or

The Fundamental Principle of Counting

Strange things on the menu here by flickr user leunix

The cafeteria special for lunch offers a choice between two main courses (hamburgers or chicken burgers) and three different drinks. The "meal deal" allows you to pick one of each. How many different "meal deals" are they offering?

What if they offer to throw in a choice of fries, spicy fries or plain chips; how many "meal deals" are they offering now?

The Fundamental Principal of CountingIf there are M ways to do a first thing and N ways to do a second thing then there are M x N ways to do both things.

Example: Any one of 4 ties can be matched with any one of 3 shirts, How many shirt and tie combinations are possible?

What if there are also 2 different pairs of pants that can be matched with all the shirts and ties, how many different "outfits" are possible now?

Now you try ...How many four-digit numbers are there if the same digit cannot be used twice?

How many four-digit numbers are there if the same digit can be repeated?

How many four-digit even numbers are there if the same digit cannot be used twice?

(a) The last part of your telephone number contains four digits. How many such four-digit numbers are there?

b) How many such four-digit numbers are there if the same digit cannot be used twice?

c) How many four-digit numbers begin with a 2 ,4 or 0 if the same digit cannot be used twice?

HOMEWORK

How many ways can the letters of the word FERMAT be arranged?

HOMEWORK