The mathematics department has 8 graduate assistants who are assigned to the same office. Each assistant is just likely to study at home as in the office. How many desks must there be in the office so that each assistant has a desk at least 90% of the time?

Mr. A lives at origin on the Cartesian plane and has his office at (4,5) His friend lives at (2,3) on the same plane. Mrs. A can go to his office travelling one block at a time either in the +y or +x direction. If all possible paths are equally likely then the probability that Mr. A passed his friends house is (shortest path for any event must be considere (a) 1/2 (b) 10/21 (c) 1/4 (d) 11/21

Meera has a housewarming party at her place. She knows that around 40 guests will turn up for the party. Calcualte the pieces of sweets she has to order so that the guests take home 4 pieces each. Also, she has 90 lamps available with her, and she wants to use them all by placing them equally on the 20 stairs leading to her house, how many more lamps does she need to buy?