NEW UNIT!

ugh! well im the scribe for today. since jeng picked me. but its okay, im fine with it...so yeea blahblah im the scribe and here are todays notes (november 15)...

first we chose a type of car...a Toyota Celica.
Colours: yellow, pink, silver, and black
Trans: Automatic or Standard

There are many possibilities for this car which is shown below :


since there are 8 possibilities to this problem...how many more if you add in the colours?

8 - possibilities
4 - colours

so.. we get 4 x 8 = 32
therefore there's 32 possible cars that can be made

we break it down like this:


if we wanted to know how many possibilities for 3 cars we could just mulitply 3 (which is how many cars we have) to the above ^^

Then mrs. ingram gave us examples which she show'd us how to do:

example 1) Shaun has 2 different shirts and 3 different pairs of pants. How many outfits can he make from these?
2 - shirts
3 - pants

2 x 3 = 6 pairs of outfits.

example 2) How many different 3-digit numbers can be made using the seven digits 1, 2, 3, 4, 5, 6, 7 without repitition?

there are 7 possibilities for all seven numbers to fit in the first spot.
since seven #'s can go there, 6 #'s are left to go into the second spot.
and if two numbers have been taken by the first two only 5 possible #'s can fit into the ones place.

like before we multiply the numbers:
7 x 6 x 5 = 210 #'s

(hard to explain but im trying)

Using the same numbers but even #'s only
(2, 4, 6 - are the even numbers)

we now know that only 3 numbers can go in the ones place.
now we know that, 6 #'s can go into the hundreds place.
and 5 #'s can go into the tens place.
we get...

6 x 5 x 3 = 90 possible even #'s

example 3) how many greater numbers than 300?
5 #'s can go into the 1st position
6 #'s in the second and
5 #'s in the third

5 x 6 x 5 = 150 #'s that are over 300

example 4) we chose 4 different bands/ singers.
1.black eyed peas
2.Wu-tang Clan
3.Madonna
4.Hulk Hogan's Daughter

we wanted to know how many different types of orders we can make out of these four cd's.

any 4 cd's can go into the first position.
so we get left with 3 cd's in the 2nd position and 2 cd's in the 3rd position and 1 in the 4th position.

we multiply all #'s to get 24 combinations
(4 x 3 x 2 x 1 = 24)

we can also write it like this : 4!

when a number is multiplied by any consecutive # after is called a factorial

Factorial- the product of consecutive natural numbers in decreasing order to the number one.

n! = n(n-1)(n-2)(n-3)...and so on.

Now we are simplifying factorial expressions

7!/3!= (7)(6)(5)(4)(3)(2)(1)/(3)(2)(1)
----= (7)(6)(5)(4)(3)(2)(1)/(3)(2)(1) : the 3, 2, 1's cancel each other
----=840

9!/5!= (9)(8)(7)(6)(5)(4)(3)(2)(1)/(5)(4)(3)(2)(1)
----= (9)(8)(7)(6)
----=3024

17!/13!=(17)(16)(15)(14)= 57120

and there you go. thats all the notes for today. hopefully you get it for those who didnt go to class. i bet you'll have a hard time understanding this. so yeea anyways. exercise 28 was assigned to us. and for those who didnt go this afternoon we just continued the exercise. yeea. thats all. k byyye! :)

OOOH! I CHOOSE.... JANET TO BE THE NEXT SCRIBE ..HEHHE..HAHAH. OKAY!