12.3 Permutations and Combinations

Mrs. TaorminaProbability and Statistics

Permutationsand

Combinations

What’s the Difference?

"My fruit salad is a combination of apples, grapes and bananas" We don't care what order the fruits are in, they could also be "bananas, grapes and apples" or "grapes, apples and bananas", its the same fruit salad.

(order does not matter) Combination

What’s the Difference?

"The combination to the safe was 472". Now we do care about the order. "724" would not work, nor would "247". It has to be exactly 4-7-2.

(Order matters) Permutation

This should be called a “permutation” lock! (You can laugh…ha! ha!)

Factorial !

7 ! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040

3 ! = 3 x 2 x 1 = 6

On Calculator: MATH PRB ! (#4)

Permutations

• This formula is used for permutations without repetition. (The FCP took care of repetition).

Number of items How many we are choosing

Combinations

• This formula is used for combinations without repetition.

Number of items How many we are choosing at a time

Pascal’s Triangle

C(0, 0)=1

C(1, 0)=1 C(1,1)=1

C(2, 0)=1 C(2,1)=2 C(2,2)=1

C(3, __) etc.

C(4, __)

C(5, __)

ASSIGNMENT:Pg. 708 #7-56

(Tuesday and Wednesday)

Calculator Steps:Enter n MATH PRB (#2-nPr) or (#3-nCr) enter r

Today at 2:00 p.m. we will be having a tornado drill. Our class must sit together in the science hallway. (Single row, sitting towards the wall, not in front of glass, with your head covered)