<p> Pascal’s Triangle Row Number Value of Sum Remark1: Pascal’s Triangle is built using an iterative process. n 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 ______</p><p>Ex. 1: Calculate the sum of the first 7 rows. Write the answers in the table above. Ex. 2: Predict the sum of the entries in rows 8 and 9 .</p><p>Pascal’s Triangle with Combinations. Pascal’s Triangle can also be written using combinations as shown below. Write the next 3 rows using 0 choose notation.   0 1 1     0 1 2 2  2       0 1  2 3 3  3  3         0 1  2  3</p><p>Ex. 4: Write an expression equivalent to:  6  6  11 a)      b)    2  3  4 </p><p>General Formula (Pascal’s Identity) </p><p>Ex. 5: Expand (a  b)n , for n  1, 2,..., 5. Ex. 6: Find the number of paths through the following letters that spell the word “COUNTING”.</p><p>C O O U U U N N N N T T T T T I I I I N N N G G</p><p>Ex. 7: A checker is placed on a game board as shown below. Determine the number of paths the checker may take to get to each allowable square on the board if it can move only diagonally forward one square at a time.</p><p>Ex. 8: How many paths lead from home to the arena? You can only move and East.</p><p>South</p><p>n n  n n Ex. 9: If       ...     512 , find n. 0 1  2 n</p><p>Homework: Pg. 289: #1-4,6-8b,12,22</p>