A computer is printing out subsets of a 5 element set (possibly including the empty set). (a) At least how many sets must be printed to be sure of having at least 3 identical subsets on the list?
(b) At least how many identical subsets are printed if there are 129 subsets on the list?

The ivring berlin learning center would like a possible net profit of $650,000 on its new resource manual it sells to schools. the fixed costs for producing the manual are $780,000 and the variable cost per package is $19.85. if the estimated unit sales are 1,250,000 units, what selling price unit should the ivring berlin learning center try?