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zvonat [6]
4 years ago
8

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

Mathematics
1 answer:
zmey [24]4 years ago
8 0
Of n elements, there are {}_nC_r=\dfrac{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=\dfrac{13!}{4!(13-4)!}=\dfrac{13!}{4!9!}
=\dfrac{13\times12\times\cdots\times6\times5}{9\times8\times\cdots\times2\times1}
=\dfrac{13\times12\times11\times10}{4\times3\times2\times1}
=13\times11\times5
=715

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