Q1.

Tina randomly selects two distinct numbers from the set { 1, 2, 3, 4, 5 }, and Sergio randomly selects a number from the set { 1, 2, ... , 10 }. What is the probability that Sergio's number is larger than the sum of the two numbers chosen by Tina?

Q2.

The number of diagonals that can be drawn in a polygon of 100 sides is:

Q3.

Six straight lines are drawn in a plane with no two parallel and no three concurrent. The number of regions into which they divide the plane is:

Q4.

Professor Gamble buys a lottery ticket, which requires that he pick six different integers from 1 through 46, inclusive. He chooses his numbers so that the sum of the base-ten logarithms of his six numbers is an integer. It so happens that the integers on the winning ticket have the same property— the sum of the base-ten logarithms is an integer. What is the probability that Professor Gamble holds the winning ticket?

Q5.

Pat is to select six cookies from a tray containing only chocolate chip, oatmeal, and peanut butter cookies. There are at least six of each of these three kinds of cookies on the tray. How many different assortments of six cookies can be selected?