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if a given set has thirteen elements how many subsets have somewhere from four through eight elements

User Asdasd
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1 Answer

4 votes
Of
n elements, there are
{}_nC_r=(n!)/(r!(n-r)!) ways of choosing any
r elements. So the number of subsets that can be chosen from the set of 13 elements, each consisting of 4 to 8 elements, is


\displaystyle\sum_(r=4)^8{}_(13)C_r={}_(13)C_4+\cdots+{}_(13)C_8=6721

To compute the actual numbers, you have, for example,


{}_(13)C_4=(13!)/(4!(13-4)!)=(13!)/(4!9!)

=(13*12*\cdots*6*5)/(9*8*\cdots*2*1)

=(13*12*11*10)/(4*3*2*1)

=13*11*5

=715

so there are 715 ways of picking subsets of size 4. Compute the others similarly, then add them up.
User Wlyles
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