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Question

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


Your Answer
A
128
Your Answer
B
125
Correct Answer
C
120
Your Answer
D
116

Solution

The correct option is D 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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