05 probability mar9
TRANSCRIPT
In how many ways can 8 books be arranged on a shelf, if 3 particular books must be together?
In how many ways can 5 people be seated in a straight line?
Factorial NotationWhen we want to multiply all the natural numbers from a particular number down to 1, we can use factorial notation to indicate this operation. The symbol "!" is used to indicate factorial. This notation can save us the trouble of writing a long list of numbers.For example:6! means 6 x 5 x 4 x 3 x 2 x 1 = 720
4! = 4 x 3 x 2 x 1 = 24
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3 628 800
1! = 1
By definition 0! = 1
On the calculator ... Press: [MATH]
[<] (Prb) [4] (!)
How many ways can 8 different CD's be arranged?
Permutations (the "Pick" Formula)
In how many ways can 5 people be seated in a straight line?
In how many ways can six students be seated in 8 vacant seats?
A permutation is an ordered arrangement of objects.
n is the number of objects available to be arranged
Examples:
On the calculator ... Press: [MATH]
[<] (Prb) [2] (nPr)
r is the number of objects that are being arranged.
In how many ways can you arrange the letters in the word HEEL
H E E L
H E E
LH E L EH E
L
EH L E EH L E E
H E E L
Permutations of nondistinguishable objects ...
Find the number of different "words" that can be made by rearranging the letters in the word:
Examples:
(a) BOOK (b) MISSISSIPPI
The number of ways to arrange n objects that contain k , k , k , ... sets of nondistinguishable objects is given by:
321
How many ways can you arrange the letters in the word
REFERENCE
7560
If there are eight cookies (4 chocolate chip, 2 oatmeal, and 2 chocolate) in how many different orders can you eat all of them?
420
There are 10 people in a competition.
How many ways can the top three be ordered?
rPn