1. FACTORIALS

2. Mathematics Definition of Factorial
The product of a given positive integer multiplied by all lesser positive integers.
Symbol: n! Where n is the given integer.

3. My Definition of Factorial
The factorial of a number is the product of all the whole numbers, except zero, that are less than or equal to that number.

4. Examples!!!!
For example, to find the factorial of 7 you would multiply together all the whole numbers, except zero, that are less than or equal to 7. Like this:
7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

5. Factorials - Cont.
The factorial of a number is shown by putting an exclamation point after that number. So, 7! Is a way of writing “ the factorial of 7 ” or
“ 7 factorial ”.
Factorials are a very useful tool in probability. They can show how many different ways there are to arrange a set of things.

6. For example, if you have 5 books on a shelf, and you want to know how many different ways there are to order or arrange them, simply find “ the factorial of 5, 5! ”
5! = 5 * 4 * 3 * 2 * 1 = 120

7. Example- Cont.
5! = 5 * 4 * 3 * 2 * 1 = 120
This shows that you can arrange 5 books 120 different ways.

8. Math Trivia!
Mathematicians have decided that the factorial of zero, or 0!, is 1.
Why?
You can arrange a set of nothing, an empty set, in just one way - as nothing, an empty set.

9. More Examples !!!
How many different hands of cards can I have if each hand can have only 5 cards in it and the order the cards were drawn is important?
Is this a permutation or a combination?

10. Permutations
Order is important
Combinations
Order is not important
Remember locker example!!

11. So, back to the problem.
How many different hands of cards can I have?
52 * 51 * 50 * 49 * 48 =
311, 875, 200

12. Would this change is you could have 4 cards in each hand?
52 * 51 * 50 * 49 =
6, 497, 400

13. Would the first and second example change if you could choose each card individually, record the result, replace the card from the deck and select another card?

14. In case 1, with 5 cards, 52 * 52 * 52 * 52 * 52 = 380,204,032
YES!!
The answer would be:
In case 1, with 5 cards,
52 * 52 * 52 * 52 * 52 =
380,204,032
In case 2, with 4 cards,
52 * 52 * 52 * 52 =
7,311,616

15. THE END!!!