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Applied 40S March 4, 2009


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Pascal's triangle and pathway problems.

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Applied 40S March 4, 2009

  1. 1. quot;How many meals?quot; or The Fundamental Principle of Counting Strange things on the menu here by flickr user leunix
  2. 2. Pascal's Triangle How many different patterns can you find in the triangle?
  3. 3. Suppose that, when you go to school from home, 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. (a) How many ways can you go to the post office? (b) How many ways can you go to school? (c) What is the probability that you will walk past the post office on your way to school?
  4. 4. How many ways can the word RIVER be found in the array of letters shown to the right if you start from the top R and move diagonally down to the bottom R? R I I V V V E E R
  5. 5. A water main broke in our neighborhood today. My kids want to get to the park to play as quickly as they can so we only walk South or East. How many different quot;shortest pathsquot; are there from our house to the park walking on the sidewalks along the streets?
  6. 6. How many ways can the word quot;MATHEMATICSquot; appear in the following array if you must spell the word in proper order? HOMEWORK
  7. 7. Find the theoretical probability of flipping three pennies and getting at least 1 heads. HOMEWORK
  8. 8. 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