Mathematical Concepts 115 ch. 11 continued

page 693 and the continuation from class notes on 2/21/09.

Factorial formula for permulations
order is important, permulations or arrangements

Permuladtions: type of arrangements=group

formula: nPr=n!
(n-r)! as a denominator

n1 objects taken r object at a time, the total # of arrangements is called total # of arrangements,

1. cannot repeat
2. order is important

for example:

10 peole
randomly are to be selected from for a 3 member committee,

3-member committee
president
Vice president
Secretary

the combinations can only be in a certain order.

ABC
BAC

formula:

10P3=10! as the numerator and
(10-3)! as the denominator= 10! over 10times 9 times 8 times 7!
7!= 7! then cancel out the 7 = 720 ways. choices.

Combination method: page 693

(objects) n taken r
as a group at a time

total number of combinations is n! over =nCr
r!(n-r)!

example for combination:

10 people
choose a 3 member committee
from a rotating committed where everyone is equal
choose 3 people from 10 for equal, how many ways.

formula is in fraction form.

10!
over 3! (10-3)!

no order only as a groups

=10!=10 times 9 times 8 times 7
over 3!= 3! and 7! because 10-3=7
cancel then calculate=
the 7's cancel in both the nominator and in the denominator
then multiple
10 times 9 times 8 times
over 3 times 2 = 120

review the pascal triangle

know page 712

table 8
n(AUB)=

Mathematical Concepts 115 ch. 11 continued

Notes on chapter 11 continued:

ex. 2
How many intergers between 1000, and 9999 divisible by 5 has 4 digits.

10 digits from 10-100.
9,10,10,2, only choose from 0-5 or two choices.
9 is 1-9, 10 is 0-9 choices,
the product rule is 9 times 10 times 10 times 10, times 2 = 1800

2. second rule: formula: factorial

0!=1
n!=1 times 2-n
1!=1
2!=1 times 2 =2
3!=1 times 2 times 3=6
4!=1 times 2 times 3 times 4 = 24

3rd rule: Factorial rule and the product rule:

example 3.

3 places or 3 boxes =

3 times 2 times 1 = 6

3 places to put people.

Arrangements of n distinct objects page 688

n=n1,+ n2, + .....nk

ex. 20 cards some cards may have 20 letters.

5 A
6 B
3 C
6 D

how many different ways to arrange the 20 symbols.

the formula for this is: n! as a numerator and n1!, n2!,....nk.

n= all summations of all of the symbols

ex. 4 (x+y+2+a+b) to the 20th power coeffecient 20

x5 power plus y7 power, plus z8 power=20

a numerator of 20! 20-19 with a demonator of 5!7!8!10!0!-5,-2 then cancel.

ex.4 continued

(a+b+c+d)8 a3b1c2d2=8 8! with a denominator of 3!1!2!2!= a numerator of

8times 7times 6 times 5 times 4 times 3 with a denominator of

3!1!2!2!= 3 times 2 times 2 times 2=

56 times 30= 1680

this is from the class notes of 2/21/09 and on page 688 of the book. Know this information for the test.

that is all for now.

I can and will do good. I will pass this test and the class. The power of positive thinking. I will do it, and I can do it.

Marie Zajac CPC

Mathematical Concepts 115 ch. 11

Chapter 11: 2/21/09 notes in class and from the text.

Discusses differant counting methods:

1. The tree diagram; page 674.
The tree diagram is a method of building numbers from a set of digits.
Foe example; A,B,C,
can be diagramed as many possible combinations availabe;
ABC, ACB, BAC, BCA, CAB, CBA,
The total number of combinations are 6.

2. The product Rule: with uniformity criterion, and the Fundamental counting principle;

ex.1. This is a multiple part task involving all parts to be the same with the same number of choices no matter what the previous choices were in the past. The formula is: n1,times n2,.....nk

another example is to have 5 choices for an I.D. card and what are all of the possibilities: = A,B,C,D, 1,2,3,
ADCC, 322 becomes the answer.

there are 4 possibilities: n1 is 4 n2 is 4 n3 is4 n4is 3 n5is 3. There are 4 possibilities, that is why n1-n3 is a 4. n-4-5 is a 3; because of the three possiblities. The product rule or the fundamental counting principle:
is n4 4.4.4.3.3 The answer is then given by the product.

That is all for now. I will continue later.

Marie Zajac with on a journey towards a bachelor's degree in psychology. I will do it.