In how many ways can a metro train have stoppage at 3 different station
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There are N
N
intermediate stations on a railway line from one terminus to another. In how many ways can a train stop at three of these intermediate stations if no two of these stopping stations are to be consecutive?
I observed that N≥5
N
≥
5
and for N=5,6,7,8,9,10
N
=
5
,
6
,
7
,
8
,
9
,
10
the answers are 1,4,10,20,35,56
1
,
4
,
10
,
20
,
35
,
56
.
Then with the aid of tetrahedral numbers, I guessed that the general answer should be (N−23)
(
N
−
2
3
)
. and this happens to be correct.
For more information please visit math.stackexchange.com
N
intermediate stations on a railway line from one terminus to another. In how many ways can a train stop at three of these intermediate stations if no two of these stopping stations are to be consecutive?
I observed that N≥5
N
≥
5
and for N=5,6,7,8,9,10
N
=
5
,
6
,
7
,
8
,
9
,
10
the answers are 1,4,10,20,35,56
1
,
4
,
10
,
20
,
35
,
56
.
Then with the aid of tetrahedral numbers, I guessed that the general answer should be (N−23)
(
N
−
2
3
)
. and this happens to be correct.
For more information please visit math.stackexchange.com
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