210k views
1 vote
You own 22 CDs. You want to randomly arrange 9 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?

User Jawann
by
7.9k points

1 Answer

5 votes
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.

User Wtrevino
by
8.3k points
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