**(1) **^{n}C_{n-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.^{n}C_{4} = 7.^{n}C_{3}

_{\(∴ 4. \frac{ni}{4i(n-4)i} = 7.\frac{ni}{3i(n-3)i}\)}

\(∴ \frac{4}{24(n-4)i}= \frac{7}{6(n-3)i}\)

\(∴ \frac{1}{6(n-4)i}= \frac{7}{6(n-3)(n-4)i}\)

\(∴ \frac{1}{6}= \frac{7}{6(n-3)}\)

∴ n - 3 = 7

∴ n = 10