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प्रश्न
Find the total number of subsets of a set with
[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] 5 elements
उत्तर
Subsets with 5 elements:
Number of subsets with no element = 5C0
Number of subsets with one element = 5C1
Number of subsets with 2 elements = 5 C2
Number of subsets with 3 elements = 5C3
Number of subjects with 4 elements = 5C4
Number of subsets with 5 elements = 5C5
Total number of subjects
= 5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5
= `1 + (5!)/(1!(5 - 1)!) + (5!)/(2!(5 - 2)!) + (5!)/(3!(5 - 3)!) + (5!)/(4!(5 - 4)!) + 1`
= `1 + (5!)/(4!) + (5!)/(2! 3!) + (5!)/(3! 2!) + (5!)/(4!) + 1`
= `1 + (5 xx 4!)/(4!) + (5 xx 4 xx 3!)/(2! xx 3!) + (5 xx 4 xx 3!)/(3! xx 2!) + (5 xx 4!)/(4!) + 1`
= `1 + 5 + (5 xx 4)/(2 xx 1) + (5 xx 4)/(2 xx 1) + 5 + 1`
= 6 + 10 + 10 + 6
= 32
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