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# Answer to Question #4738 in Combinatorics | Number Theory for Hussain Mirza

Question #4738
How many subsets does the set {a1,a2,...,an} of n elements have? How many subets are the containing the element a1? Prove your claim.
1
2011-10-20T08:26:01-0400
First we need to formalize this& problem.
Let's consider sequence with n elements that consists with 0 and 1. Let
x={x1,x2,...xn}, xi є{0,1}, i=1,...n
If some element enters into some set we will designate it 1 in sequence& .
On each place can be 0 or 1 (two possibilities), we have n positions, then let's count all possible variants
Then the set {a1,a2,...an} of n elements have& 2^n subsets.
About& a1 . Let's fix the first position in sequence& . We have x={1,x2,...xn}
Let's calculate all possible variants
The first position is fixed.
2^(n-1) subsets contain the element a1

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