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Question
Find the total number of subsets of a set with
[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] n elements
Solution
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 …………… nCn respectively.
∴ Total number of subjects = nC0 + nC1 + nC2 + nC3 + ………… + nCn
= Sum of the coefficients in the binomial expansion (x + a)n
= 2n
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