(1) nCn-2 = 15
∴ \(\frac{n!}{(n−2)!(n−n+2)!}\) = 15
∴ \(\frac{n(n−1)(n−2)!}{(n−2)!2!}\) = 15
∴ \(\frac{n(n−1)}{2}\) = 15
∴ n(n – 1) = 30
∴ n(n – 1) = 6 × 5
∴ n(n – 1) = 6(6 – 1)
∴ n = 6
(2) 4.nC4 = 7.nC3
\(∴ 4. \frac{ni}{4i(n-4)i} = 7.\frac{ni}{3i(n-3)i}\)
\(∴ \frac{4}{24(n-4)i}= \frac{7}{6(n-3)i}\)
\(∴ \frac{1}{6(n-4)i}= \frac{7}{6(n-3)(n-4)i}\)
\(∴ \frac{1}{6}= \frac{7}{6(n-3)}\)
∴ n - 3 = 7
∴ n = 10
