Sec
20.3
Permutations
Permutations
permutation is
obji Understand what
Sec
20.3
permutation
Permutations
Presidency
Yo
order matters
-
4 How many ways
!
=3
-21
3-
.
letters A
the
can
.
List them
use
a
.
ordering of objects
.
how to
&
a
!
h
n
=
(n
.
.
1)
(n
.
C be
a
distinct objects is
n
,
B
,
ordered ?
6
=
In general the permutation of
repetition
)
z
.
3.2
r
.
.
.
.
.
:
1
Factorial
5 !
4.
4
.
=
!
18
6.402
'
-
Ex a) How many
-
b)
.
.
different
12
How many
ways can
12 skiers taken
-
npr
Ex
.
a)
.
=
1015
x
!
3
3
skiers finish
,
it
121
,
=
€
=
.
Calculate the following permutations
•
P
}
:
:
2nd
,
b
)
, o
Pz
.
:
a
competition ?
51 ?
a
10
II
ways
Ed
finish
12 skiers
can
ways
6.40×1015
=
1320
÷
'a¥
'
.
2759¥
Ex
.
considering 10 different colleges
visit 6 of the colleges ?
you
5bLOP
-9-8
7I
=
You
are
can
.
In how
my
orders
6
Permutationsulrepetitionq
,#iq
I
!
obj
.
is repeated q times
,
of the letters in the
6. find the # of distinguishable permutations
a) Puppy
b)
4.3
.
.
.
2!
z t
Y
happens
z
;
z
( n il
.
!
=
f ( z)
f( oh ) )
It
.
=
5
4.3
.
10080
=
I
.
.
I
(5-1) !
Function notation
2+3
FG )
×
=
.
.§Efy
¥¥3
rs
→
2
:
;
.
circular permutations ?
A
circular
6
.
=
,
word
=
8.7
#z
5jl¥
#
*z÷
zo
=
81
MISSOURI
4!
what
5¥
=
another qztimes
,
-
f(z)~
ffs )
.
g (2)
51,3
4
'
gk )
3=7
Same
=[
2( 2)
.
.
/
different ?
!
Zx
.
or
I
-
-
I
=
fog
3
G)
=
FGKD