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प्रश्न
Find the total number of subsets of a set with
[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] 4 elements
उत्तर
Subsets with 4 elements
Number of subsets with no element = 4Co
Number of subsets with one element = 4C1
Number of subsets with two elements = 4C2
Number of subsets with three elements = 4C3
Number of subsets with four elements = 4C4
∴ Total number of subsets
= 4C0 + 4C1 + 4C2 + 4C3 + 4C4
= `(4!)/(0!(4 - 0)!) + (4!)/(1!(4 - 1)!) + (4!)/(2!(4 - 2)!) + (4!)/(3!(4 - 3)!) + (4!)/(4!(4 - 4)!)`
= `(4!)/(4!) + (4!)/(3!) (4!)/(2! xx 2!) + (4!)/(3! xx 1!) + (4!)/(4! xx 0!)`
= `1 + (4 xx 3!)/(3!) + (4 xx 3 xx 2!)/(2 xx 1 xx 2!) + (4 xx 3!)/(3!) + (4!)/(4!)`
= 1 + 4 + 6 + 4 + 1
= 16
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