Question

If ⁿC₂ = 15, then find the value of n.

Answer 1

ⁿC₂ = 15

∴ \(\frac{n!}{2!(n−2)!}\) = 15

∴ \(\frac{n(n−1)(n−2)!}{2⋅(n−2)!}\) = 15

∴ n(n – 1) = 15 × 2

∴ n(n- 1) = 30 = 6 × 5

∴ n[n – 1) = 6(6-1)

∴ n = 6