FACTORIALS
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 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 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 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.
• 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 = 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 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 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
• Remember locker example!!
• 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?
• 52 * 51 * 50 * 49 =
• 6, 497, 400
• 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 cards,
• 52 * 52 * 52 * 52 * 52 =
• 380,204,032
• In case 2, with 4 cards,
• 52 * 52 * 52 * 52 =
• 7,311,616
THE END!!!