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2007 Cyprus MO/Lyceum/Problem 18

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
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
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