The maximum number of permutations of 2n letters in which there are only a’s and b’s…
Mathematics · JEE Advanced · NTA Exams — Permutations and Combinations
The maximum number of permutations of 2n letters in which there are only a’s and b’s, taken all at a time is given by :
- 2nCn
- \(\frac{2}{1} \cdot \frac{6}{2} \cdot \frac{0}{3} \ldots \cdot \frac{4 n-6}{n-1} \cdot \frac{4 n-2}{n}\)
- \(\frac{n+1}{1} \cdot \frac{n+2}{2} \cdot \frac{n+3}{3} \cdot \frac{n+4}{4} \cdot \ldots \cdot \frac{2 n-1}{n-1} \cdot \frac{2 n}{n}\)
- \(\frac{2^{n}[1 \cdot 3 \cdot 5 \ldots(2 n-3 \check{\ell} 2 n-1)]}{n!}\)
Answer
(A) 2n C n, (B) 2 1 6 2 0 3 4 n-6 n-1 4 n-2 n, (C) n+1 1 n+2 2 n+3 3 n+4 4 2 n-1 n-1 2 n n, (D) 2^ n [1 3 5 (2 n-3 2 n-1)] n!
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