Five friends went to a local restaurant and all had the buffet at $6.75 each. two friends added ice cream for dessert for $1.99 each. the following is their restaurant bill. does it seem reasonable? $6.75 + $6.75 + $6.75 + $6.75 + $6.75 + $1.99 + $1.99 = $37.73

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 ?