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Problem
Problem
Number of ways in which three numbers in AP can be selected from 1, 2, 3, ..., n, is a.
(
n
−
1
2
)
\binom{n-1}{2}
(
2
n
−
1
)
, if n is even b.
n
(
n
−
2
)
4
\frac{n(n-2)}{4}
4
n
(
n
−
2
)
, if n is even c.
n
(
n
−
1
)
4
\frac{n(n-1)}{4}
4
n
(
n
−
1
)
, if n is odd d.
n
(
n
+
1
)
2
\frac{n(n+1)}{2}
2
n
(
n
+
1
)
, if n is odd
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