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

1 Answer

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


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


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