1. Formulas for C ( n,r ) 2. Binominal Coefficient 3. Binomial Theorem 4. Number of Subsets 1.

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Presentation transcript:

1. Formulas for C ( n,r ) 2. Binominal Coefficient 3. Binomial Theorem 4. Number of Subsets 1

2

 Work the route problem covered previously by selecting where in the string of length 7 the 4 E’s will be placed instead of the 3 S’s.  Therefore the total number of possible routes is 3 Notice that C(7,4) = C (7,3).

 Another notation for C ( n,r ) is. 4 is called a binominal coefficient.

5

 Binomial Theorem 6

 Expand ( x + y ) 5. 7 (x + y ) 5 = x 5 + 5x 4 y + 10x 3 y x 2 y 3 + 5xy 4 + y 5

 A set with n elements has 2 n subsets. 8

 A pizza parlor offers a plain cheese pizza to which any number of six possible toppings can be added. How many different pizzas can be ordered?  Ordering a pizza requires selecting a subset of the 6 possible toppings.  There are 2 6 = 64 different pizzas. 9

 C(n,r ) is also denoted by.  The formula C(n,r ) = C(n,n - r ) simplifies the computation of C(n,r ) when r is greater than n /2.  The binomial theorem states that 10

 A set with n elements has 2 n subsets. 11