Combinations Binomial Theorem Pascal's Triangle

12.2 Combinations and Binomial Thm p. 708

In the last section we learned counting problems where order was important ,[object Object],[object Object]

A Combination is a selection of r objects from a group of n objects where order is not important

Combination of n objects taken r at a time ,[object Object]

Finding Combinations ,[object Object],[object Object],[object Object],= 2,598,960

In how many of these hands are all 5 cards the same suit? ,[object Object],[object Object]

How many 7 card hands are possible? ,[object Object]

[object Object],[object Object]

Deciding to + or * ,[object Object],[object Object]

Suppose you can afford at most 3 ingredients ,[object Object],[object Object]

Subtracting instead of adding: ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object]

The Binomial Theorem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Pascal's Triangle! ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

(a+b) n (n is a positive integer)= ,[object Object],[object Object]

(a+3) 5 = ,[object Object],[object Object]

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