Question

Find the total number of subsets of a set with
[Hint: ⁿC₀ + ⁿC₁ + ⁿC₂ + ... + ⁿCn = 2ⁿ] n elements

Answer 1

Subsets with n elements

Number of subsets with no element = nC₀

Number of subsets with 1, 2, 3, 4, …………. n elements are nC₁, nC₂, nC₃, nC₄ …………… nC_n respectively.

∴ Total number of subjects = nC₀ + nC₁ + nC₂ + nC₃ + ………… + nC_n

= Sum of the coefficients in the binomial expansion (x + a)ⁿ

= 2ⁿ