Yay!!! We continue the lessons of Counting.
Today we will do basic counting of certain objects.
Example 1:
How many ways can you arrange the letters in the word: WORD.
Lets see how to figure this question out.
For the first letter, there are 4 possiblities, W, O, R or D.
So 4 _ _ _
Now we have 3 left over:
4 3 _ _
And it continues to 4,3,2,1, which is 24.
This is also known as factorials.
4! (!=factorial) =24
W-O-R-D
W-O-D-R
W-R-O-D
W-R-D-O
W-D-O-R
W-D-R-O
continued...
Here is a table of some factorials.
1!=1
2!=2
3!=6
4!=24
5!=120
6!=720
7!=5040
...
Now lets look at another problem.
Example 2:
Coins.
How many outcomes are there for 3 coins?
For the first coin, we either have a head or a tail. (H,T)
Using the same method as above, we have 2x2=4
These are just powers of 2.