Your cousin, who is planning her wedding, is working on the seating chart for the reception. she is trying to decide which 6 people should be seated at the table closest to the head table. she has narrowed her decision down to a list of 10 friends. if the order doesn't matter, in how many ways can she choose 6 friends from the list of 10 to sit at the table closest to the head table?

Acompany manufactures three types of cabinets. it makes 110 cabinets each week. in the first week, the sum of the number of type-1 cabinets and twice the number of type-2 cabinets produced was 10 more than the number of type-3 cabinets produced. the next week, the number of type-1 cabinets produced was three times more than in the first week, no type-2 cabinets were produced, and the number of type-3 cabinets produced was the same as in the previous week.