A dance student wants to know the favorite type of dance class for students at The Dance Academy. She surveys each student in her ballet class. In which way could the results of her survey be most improved? She could sample an equal number of students in each type of dance class. She could sample a proportional number of students in each type of dance class. She could sample one student in each type of dance class. She could sample one teacher from each type of dance class.

Exercise: counting committees 0.0/2.0 puntos (calificable) we start with a pool of n people. a chaired committee consists of k≥1 members, out of whom one member is designated as the chairperson. the expression k(nk) can be interpreted as the number of possible chaired committees with k members. this is because we have (nk) choices for the k members, and once the members are chosen, there are then k choices for the chairperson. thus, c=∑k=1nk(nk) is the total number of possible chaired committees of any size. find the value of c (as a function of n ) by thinking about a different way of forming a chaired committee: first choose the chairperson, then choose the other members of the committee. the answer is of the form c=(α+nβ)2γn+δ. what are the values of α , β , γ , and δ ?