Number of ways in which 3 different numbers in A.P. can be selected from 1, 2, 3,...... n is:
if n is even
if n is odd
if n is odd
if n is even
Text Solution
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(c,d)
Here given no. be 1,2,3,.........n
Let common difference = r
Total way of selection = (1, 1 + r, 1+2r),(2, 2 + r, 2 + 2r), ..(n – 2r, n – r, n)
Total numbers are = (n – 2r)
Here r min. = 1 and r max. = (n – 1)/2
Case- I When n is odd
∴ r max = 
& total no. of selection is = 
= 
– 
= 
Case - II when n is even = r max = 
so total no. selection is
= 
= 
– 
= 
= 
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