Transcript factorials

What we’ve done
so far…
If we want to put a math textbook
and a math workbook in
two different lockers, there are 2
ways to do it:
The math textbook can go into one locker
or the other, and then the math workbook
can go into the remaining locker.
If we add a third book and a
third locker, there are now more
possibilities.
The math textbook can go in the first,
second, or third locker, leaving two books to
place in the two remaining lockers.
As a result, there are
6=321
ways to arrange the three books.
If we add a forth book and a
forth locker, there will now be 4
places to put the new book.
For each of these four possibilities,
there will be six ways to arrange the
remaining three books.
Therefore, 24 = 4  3  2  1
ways to arrange the three books.
FACTORIAL
What is Factorial?
• The Factorial of a specified number
refers to the product of a given series
of consecutive whole numbers
beginning with 1 and ending with the
specified number
• We use the “!” to represent factorial
Eg.
5! = 1  2  3  4  5 = 120
It’s A Fact!
The number of ways of arranging
n objects is n!
n! = n  (n − 1)  (n − 2)  . . .  3  2  1
Calculators
Try these on your calculators.
6
9
x!
x!
=

8
720
x!
=
When do we use calculators and when is it better to do
mental calculation?
9
Which is greater?
8
x!
40320
or

4
x
65536
8
Which is greater?
7
x!
=
5040
2
x

3
x
or
5
6
5400
=