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)=