Counting

Hello everyone! For today's class we started off with Mr. K teaching us how to count in bases. 

First off, we started off with learning how to count with base ten. 

We had the numbers : 0 1 2 3 4 5 6 7 8 9  to work with.  

What he showed us was that from a 10, you start off from the right going to the left. To make this more clear I'll show you all. 

From here we started off with the zero. What we know is that ten to the power of zero is equaled to 1 from there we take the zero and multiply it to ten to the power of zero. 

That there we find out that we would have one-zero. 

Then we would move on to the left, to the one and you would do the exact same thing. 

So now instead of doing ten to the power of zero, we would have ten to the power of one. 

Ten to the power of one would equal to 10. So you have one-ten.  

Here is another example to try to make this more clearer. 

Say I put down 1 2 3 5. 

Then you would have 5 "ones"

3 "tens"

2 "hundreds"

1 "thousand"

Each of these steps is a multiplied by ten. Showing you that it is a base ten. But the one that we will use most would be base two. 

x2^4 = 16     x2^3=8     x2^2=4     x2^1=2     x2^0=1     

That's what I believe we ended with for counting bases. 

Then we moved on to the fundamental principle of counting. 

We first went over our homework that was assigned to us. 

We were taught about factorial. 

Ex. 

8*7*6*5*4*3*2*1 = 40 320

Instead of going doing all that work, he also showed us how to do it on the calculator. 

What you have to do is punch in 8. 

Once you see the number 8 on your screen, you press the button MATH. 

In there you press your arrow key to the left and that would take you to probability. 

When you are there, you would see a exclamation mark. "!" That's what you want to press. 

Hit enter and it would lead you to the main screen. If you hit enter again, it would give you the answer. 

8! = 40 320

What we also found out is that when you do 0!

Then it would equal to one. 

0! = 1 Has been assigned as a DEFINITION. 

When given a question like that, do not write it like so:

10! = 10*9*8*7*6*5*4*3*2*1 = 3 628 800

This is not the proper way to show it. 

After all of the homework review, we also did a group work. 

First question was, How many 4 digit numbers are there in which all the digits are different. 

_  _  _  _ 

Well what I did was that I figured that there are ten numbers, but since you can't use 0 as the first number of the digits, then you would have 9 numbers that you are able to use.  So there are 9 possible numbers that you can use for the first digit. 

9  _  _  _ 

For the second digit slot, you can now use the 0. So you have another 9 options that you are able to put in the second slot because you already used a number in the first slot and you are not able to use it again. So it would look like this:

9  9  _  _

Then for the next one it would be an 8 because you have used another number that is not able to be used again, and so on. 

Then it would be :

9  9  8  7

What you would do with these numbers is you would multiply them together. 

9 * 9 * 8 * 7

That would give us 4536 different ways to put four different digit numbers together. 

The next question is: How many of these digits are odd?

_  _  _  _

What you have to do is figure what odd numbers are there. It would be 1, 3, 5, 7, and 9. There are five odd numbers, so what you would have to do is place a five at the end of the digits like so: 

_  _  _  5

Now that you know how many odd numbers, then you can figure out how many numbers can go into the first digit. Since you used 1 odd number and you can not use a 0 in the first digit, then you only have 8 possibilities of any of the other numbers being in the first digit.

8  _  _  5

For the second digit, you can now use the 0 so the number of possibilities would be 8 again. 

After that the numbers cannot be used again, so the third digit has 7 possibilities. Then it would be : 

8  8  7  5 

Now you multiply them together and you get 2240 possibilities. 

That is what I basically remembered from today's class. 

It's the weekend so have fun! 

But don't forget to also DO YOUR HOMEWORK! 

Next scribe will be ... CAMILLA! =)