Permutation and CombinationHard
Question
Number of ways in which 3 numbers in A.P. can be selected from 1, 2, 3,...... n is:
Options
A.
if n is even
if n is evenB.
if n is odd
if n is oddC.
if n is odd
if n is oddD.
if n is even
if n is evenSolution
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 rmin. = 1 and rmax. = (n - 1)/2
Case- I When n is odd
∴ rmax =
& total no. of selection is
Case - II when n is even = rmax =
so total no. selection is
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 rmin. = 1 and rmax. = (n - 1)/2
Case- I When n is odd
∴ rmax =
& total no. of selection isCase - II when n is even = rmax =
so total no. selection is
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