1. The document discusses using the nCr formula to calculate probabilities and routes between different locations on a grid. 2. It provides an example of calculating the probability of reaching Granny's house given the presence of a gang blocking some routes. 3. The key steps are using nCr to calculate the total number of routes between locations, finding the number of "blocked" routes, and dividing the number of "safe" routes by the total to get the probability.

1. Mr. Pitto 12 th Grade Math

2. Memorize the nCr formula as a backup for not having a calculator on hand Develop an understanding for the different components of the nCr formula. More practice on calculating probability

3. The Latin Kings are a local gang and happen to be roaming the streets between your house and Granny’s house. Those who dare cross their path, have been rumored to disappear forever! Will you make it to Granny’s birthday party?

4. Before we can start problem solving, we must learn the background information that our calculator has been doing for us the last few days. You already know how to use the nCr key on your TI-83 calculator, but what if you don’t have a calculator? We need to know how to do the calculations ourselves! Here is the nCr formula: n!__ r!(n-r)! n = your population r = number of elements chosen from n

5. The diagram of the neighborhood is a 10 x 10 block grid. Granny’s House on the NE corner (top right) and your house on the SW corner (bottom left). The Latin Kings are located 4 blocks East and 3 blocks North (4 blocks right, 3 blocks up). Remember, at each intersection you can only move North or East until you reach Granny’s house, there is NO backtracking. Create a grid to help picture this scenario. Example -> Must add labels…

6. What is the probability that you will make it to Granny’s birthday party? BRAINSTORM… What do we know? What do we think we know? What do we need to know?

7. 1. You have to travel 10 blocks E and 10 blocks N to get to Granny’s house. 2. You have to travel 4 blocks E and 3 blocks N to get to Latin Kings. 3. You have to travel 6 blocks E and 7 blocks N to get from Latin Kings to Granny’s house. 4. For every route from your house to Latin Kings can be matched up with every route from Latin Kings to Granny’s, so they are independent events

8. 1. We need to use nCr formula to find out the total number of routes for each of the 3 travels. 2. You have to travel a total of 20 blocks to get to Granny’s, 10 of which are East. 3. You have to travel a total of 7 blocks to get to Latin Kings, 4 of which are East.. 4. You have to travel a total of 13 blocks to go from Latin Kings to Granny’s, 6 of which are East. 5. Because going from your house to Latin Kings and going from Latin Kings to Granny’s are independent events, you multiply the 2 answers together to find total number of routes to Granny’s that go through the Latin Kings.

9. 1. Total number of routes to get from your house to Latin Kings. 2. Total number of routes to get from Latin Kings to Granny’s house. 3. Total number of routes to get to Granny’s house. 4. Total number of “safe” routes to get to Granny’s house.

10. Total number of routes from your house to the Latin Kings if n = 7 and r = 3? Total number of routes from Latin Kings to Granny’s if n = 13 and r = 6? Total number of routes from your house to Granny’s if n = 20 and r = 10? REMEMBER THE FORMULA????

11. According to our calculations, there should be 184,756 total routes from your house to Granny’s house. Also according to our calculations, there should be 60,060 total routes from your house to Granny’s house that cross paths with the Latin Kings. To find the number of “safe” routes from your house to Granny’s you simply subtract the 2totals because you either cross paths with them or you don’t. Therefore 184,756 – 60,060 =124,696 so there are 124,696 total “safe” routes to Granny’s. 124,696 = approximately 0.675 184,756

12. Memorize the nCr formula as a backup for not having a calculator on hand Develop an understanding for the different components of the nCr formula. More practice on calculating probability

13. Name and date a Microsoft Word document, showing all work, and email me the finished product by the due date (jrp5i@mtmail.mtsu.edu) There is a 16 x 16 block grid (just like this exercise, but slightly larger) with school on the NW corner and your house on the SE corner. There is an giant car wreck at the intersection 5 blocks North and 9 blocks West. You heard on the radio that there was a wreck but you didn’t catch where it was, and you need to avoid that intersection to make it to school on time. What is the probability you take a random route to school and make it on-time?