After the tas run out of food, head ta hannah makes the executive decision to call up n distinct catering companies. each catering company has exactly 2 specialty dishes (one spicy dish and one non-spicy dish), each of which hannah can either buy or refuse to buy. however, hannah doesn't want the food selection to be boring, so she doesn't want to buy two dishes from the same company. since the tas have started complaining, she wants to order at least one dish for the cookout. in how many ways can she do this? 6. (15 pts) andy is cooking steak on the grill and he has 13 different spices that he wants to add to the steak. after carefully examining them for their fragrant qualities and compatibility, he lines them up and labels them from 1 to 13. to best bring out the flavors, a spice i must be added before (not necessarily immediately) at least one of spice i +1 or spice i - 1, if they exist, unless spice i is the last spice added to the steak. for example, spice 1 cannot be added before "spice 0" to satisfy the flavor ordering, since "spice 0" does not exist. then, spice 1 must be added before spice 2, unless spice 1 is added last. however, spice 2 may be added before spice 1 or spice 3 (or both) to satisfy the flavor ordering, unless spice 2 is added last. in how many orders can andy add all 13 spices to his steak to bring out the best flavors?