4
P
2
4
3
2
2
1
1
Cancel out the 2
1 from the numerator and denominator.
4
P
2
4
3
4
P
2
12
Therefore, there are 12 ways to arrange the letters
ABCD
in groups of two:
AB
AC
AD
BA
BC
BD
CA
CB
CD
DA
DB
DC
Practice Question
Casey has four different tickets to give away to friends for a play she is acting in. There are eight friends
who want to use the tickets. How many different ways can Casey distribute four tickets among her eight
friends?
a.
24
b.
32
c.
336
d.
1,680
e.
40,320
Answer
d.
To answer this permutation question, you must use the formula
n
P
r
(
n
n
!
r
)!
, where
n
the number
of friends
8 and
r
the number of tickets that the friends can use
4. Plug the numbers into the
formula:
n
P
r
(
n
n
!
r
)!
8
P
4
(8
8!
4)!
8
P
4
8
4
!
!
8
P
4
Cancel out the 4
3
2
1 from the numerator and denominator.
8
P
4
8
7
6
5
8
P
4
1,680
Therefore, there are 1,680 permutations of friends that she can give the four different tickets to.
C o m b i n a t i o n s
Some questions ask you to determine the number of ways to arrange
n
items in groups of
r
items without
repeated items. In other words,
the order of the items doesn’t matter.
For example, to determine the number of ways
to arrange the letters
ABCD
in groups of two letters in which the order doesn’t matter, you would count only
AB
,
not both
AB
and
BA
. These questions ask for the total number of
combinations
of items.
8
7
6
5
4
3
2
1
4
3
2
1
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