FACTORIALS Mathematics Definition of Factorial The product of

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FACTORIALS

FACTORIALS

Mathematics Definition of Factorial • The product of a given positive integer multiplied by

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.

My Definition of Factorial • The factorial of a number is the product of

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.

Examples!!!! • For example, to find the factorial of 7 you would multiply together

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

Factorials - Cont. • The factorial of a number is shown by putting an

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 many different ways there are to arrange a set of things.

• For example, if you have 5 books on a shelf, and you

• 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

Example- Cont. • 5! = 5 * 4 * 3 * 2 * 1

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

Math Trivia! • Mathematicians have decided that the factorial of zero, or 0!, is

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.

More Examples !!! • How many different hands of cards can I have if

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?

• Permutations • Order is important • Combinations • Order is not important

• Permutations • Order is important • Combinations • Order is not important • Remember locker example!!

• So, back to the problem. • How many different hands of cards

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

• Would this change is you could have 4 cards in each hand?

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

• Would the first and second example change if you could choose each

• 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?

• YES!! • The answer would be: • In case 1, with 5

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

THE END!!!

THE END!!!

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