According to the question, 9 out of 23 CDs are selected. This selection can be done in
23
C
9
ways.
The total number of possible arrangements:
23
C
9
=
23
!
(
23
−
9
)
!
9
!
=
23
!
9
!
14
!
There is only one possible arrangement of Cds in alphabetic order. The probability that the CDs are in alphabetic order is:
P
r
o
b
a
b
i
l
i
t
y
=
1
23
!
9
!
14
!
P
r
o
b
a
b
i
l
i
t
y
=
9
!
14
!
23
!
P
r
o
b
a
b
i
l
i
t
y
=
9
×
8
×
7
×
6
×
5
×
4
×
3
×
2
×
14
!
23
×
22
×
21
×
20
×
19
×
18
×
17
×
16
×
15
×
14
!
P
r
o
b
a
b
i
l
i
t
y
=
1
23
×
19
×
11
×
15
×
17
×
14
P
r
o
b
a
b
i
l
i
t
y
=
1
17160990
P
r
o
b
a
b
i
l
i
t
y
≈
0.00000000587
The probability that the rack ends up in alphabetical order is about
0.00000000587.