2007 Cyprus MO/Lyceum/Problem 18

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Problem

How many subsets are there for the set $A=\{1,2,3,4,5,6,7\}$?

$\mathrm{(A) \ } 7\qquad \mathrm{(B) \ } 14\qquad \mathrm{(C) \ } 49\qquad \mathrm{(D) \ } 64\qquad \mathrm{(E) \ } 128$

Solution

$\binom{7}{0}+\binom{7}{1}+\ldots+\binom{7}{7}=2^7=128\Longrightarrow\mathrm{ E}$

See also

2007 Cyprus MO, Lyceum (Problems)
Preceded by
Problem 17
Followed by
Problem 19
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