(1) nC2 = 28
nC2 = 28
∴ \(\frac{n!}{2!(n−2)!}\) = 28
∴ \(\frac{n(n−1)(n−2)!}{2×(n−2)!}\) = 28
∴ n(n – 1) = 28 × 2
∴ n(n – 1) = 56
∴ n(n – 1) = 8 × 7
∴ n(n – 1) = 8(8 – 1)
∴ n = 8
(2) 27Cr+4 = 27C2r-1
27Cr+4 = 27C2r-1
nCx = nCy
Or
n = x + y
27Cr+4 = 27C2r-1
∴ r + 4 = 2r – 1
∴ 4 + 1 = 2r – r
∴ r = 5
Or
r + 4 + 2r – 1 = 27
∴ 3r + 3 = 27
∴ 3r = 27 – 3
∴ r = 24 / 3 = 8