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Question

Mathematics Question on permutations and combinations

If 2nC3 : nC3 = 10, then n2+3nn2−3n+4\frac{n^{2}+3n}{n^{2}-3n+4} is equal to

Answer

2nC3nC3=10⇒2n.(2n−1).(2n−2)n.(n−1)(n−2)\frac{^{2n}C_{3}}{^{n}C_{3}}=10\Rightarrow \frac{2n.(2n-1).(2n-2)}{n.(n-1)(n-2)}
⇒(2n−1).2n−2\Rightarrow \frac{(2n-1).2}{n-2}
⇒n=8\Rightarrow n=8
Therefore, n2+3nn2−3n+4\frac{n^{2}+3n}{n^{2}-3n+4} = 8844\frac{88}{44} = 2

The answer is 2