# Math SAT/PSAT Prep

Home of the Hyman Maneuver

# Example Handout

Counting Problems

The fundamental counting principle is the principle by which you figure out how many possibilities there are for selecting members of different groups:

If one event can happen in n ways, and a second, independent event can happen in m ways, the total ways in which the two events can happen is n times m. If you flip a coin and roll a die, the total number of outcomes is 12 because a coin has 2 sides and a die has 6 sides and the total number of outcomes is 2 times 6. If you flip two coins and roll a die, the total number of outcomes is 24 because the first coin has 2 sides, the second coin has 2 sides and the die has 6, making the total number of outcomes 2x2x6=24.

If you select member after member from the same group, the number of possible choices will decrease by 1 for each choice. Some counting problems involve permutations. A permutation of a set is a reordering of the elements in the set. A combination of a set is a reordering of the elements in the set in which the order that the members are chosen doesn’t matter.

Logical Reasoning

Some mathematics questions emphasize logical thinking. You have to figure out how to draw conclusions from a set of facts.

Stacey, Carla, Julia and Rose want to take seats in a cinema. There is only 1 isle seat and the rest are in a line next to it. If Rose want to sit in the isle seat, Julia wants to sit next to Stacey, and Carla doesn’t want to sit next to Julia, how will they sit (starting at the isle)?

1. Rose, Julia, Stacey, Carla
2. Rosa Carla, Julia, Stacey
3. Stacey, Carla, Julia, Rose
4. Rose, Stacey, Julia, Carla