What is the minimum number of students, each of whom comes from one of the 5 boroughs, who must be enrolled in a class to guarantee that there are at least 15 who come from the same borough? Justify.
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- The number of 5-element subsets from a set containing n elements is equal to the number of 6-element subsets from the same set. What is the value of n? (Hint: the order in which the elements for the subsets are chosen is not important.)To allocate annual bonuses, a manager must choose his top four employees and rank them first to fourth. In how many ways can he create the ‘Top- Four” list out of the 32 employees?