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Question

A set S has 7 elements. How many subsets having at most 5 elements does it have?

A
128
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B
125
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C
120
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D
116
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Solution

The correct option is C 120
Number of subsets of S = n (P(S))
n(S)=7 n(P(S))=27=128
The number of 7 element subsets of S =1 (S itself). 6 elements subsets of S are obtained by removing 1 element in S and this can be done is 7 ways.
The number of 6 element subsets of S =7.
The number of subsets of S with at most 5 elements = 128-7-1 =120

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