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