Pascals Triangle 1 The number 2 is written next to point B2

Pascal\'s Triangle:

1. The number 2 is written next to point B2. what are two different ways you can get from point A1 to Point B2??

2. copy the grid. Travel only down or to the right. In how many ways can you get from point A1 to Point A3??

3. Use your copy of the grid from exercise 2. In how many ways can you get from point A1 to point C2??

4. In how many ways can you get to the fountain at point E6 from your starting point A1??

5. Mark the number of ways you can get to each point from A1.

6. Describe any patterns you see in the numbers on the grid??

7. The completed grid is called Pascal\'s triangle. rotate your copy of the grid 45degree clockwise so that point A1 is at the top. Explain why the grid is called a triangle

You are here. A B C D EF G H 2 2 3 5 6 7 8

Solution

1) The two ways to reach from A1 to B2 are:

2) If we can only move \"Down\" and \"Right\", then there is only one way to go from A1 to A3

All other ways will involve first going to the right and then coming back to the left. Since moving towards left is not allowed, therefore, no other possibility is available.

3) There are three ways to get from A1 to C2

4)Total ways to go from A1 to E6 are 62:

Likewise there will be total 62 ways. (The pattern is 6c1+6c2+6c3+6c4+6c5)