1. If a student is to answer any six problems on a test consisting of nine problems, in how many ways can the student select the six problems? 2. There are 7 people in a dinner gathering. In how many ways can the host (one of the 7) arrange his guests in a dining table if a they can sit on any of the chairs? b 3 people insist on sitting beside each other? c. 2 people refuse to sit beside each other? 3. From 6 Algebra books and 8 Trigonometry books, in how many ways can a student selects 3 Algebra and 3 Trigonometry books to buy if all the said books are equally necessary?​