Correct Answer - D
The total number of ways of choosing 3 stations out of n stations is
.
n
C
3
.
.
So, total number of ways
=
.
n
C
3
=
.
Let
x
1
x
be the number of stations before the first halting stations,
x
2
x
between first and second,
x
3
x
between second and third and
x
4
x
on the right of third station. Then,
x
1
≥
0
,
x
2
≥
1
,
x
3
≥
1
and
x
4
≥
0
x
such that
x
1
+
x
2
+
x
3
+
x
4
=
n
−
3
x
The total number of solutions of this equation is
.
n
−
2
C
3
.
.
Hence, required probability
=
.
n
−
2
C
3
.
n
C
3
=
(
n
−
3
)
(
n
−
4
)
n
(
n
−
1
)
=
