Number of ways in which 3 numbers in A.P. can be selected from 1, 2, 3, ...... n is :
Mathematics · JEE Advanced · NTA Exams — Permutations and Combinations
Number of ways in which 3 numbers in A.P. can be selected from 1, 2, 3, ...... n is :
- \(\left(\frac{\mathrm{n}-1}{2}\right)^{2}\) if n is odd
- \(\frac{\mathrm{n}(\mathrm{n}-2)}{4}\) if n is odd
- \(\frac{(\mathrm{n}-1)^{2}}{4}\) if n is odd
- \(\frac{\mathrm{n}(\mathrm{n}-2)}{4}\) if n is even
Answer
(A) ( n -1 2 )^ 2 if n is odd, (D) n ( n -2) 4 if n is even
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