practice problems pending

 Q1) Find the number of ways in which three numbers in A.P. can be selected from (1, 2, 3, ..., n). (For both (n) odd and even.)
S1)
We have to select 2 numbers of same parity and the AM will lie within.
Case 1: n is even.
Select 2 odd numbers: (n/2)C2
Select 2 even numbers: same

Case 2: n is odd.
Select 2 odd numbers: (n+1)/2C2
Select 2 even numbers: (n-1)/2C2

simplify to get:
(n-1)^2/4

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